The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [-1, 1], [0, 0], [0, 1]} is to equal 4 2 q (q - 1) - ------------- 2 4 1 - 3 q + q It took, .101, seconds of CPU time The first 20 terms are [1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229, 1346269, 3524578, 9227465, 24157817] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[0, 0], [0, 1], [1, 0], [1, 1]} is to equal 2 2 2 1/2 2 1/2 -3 q + q (1 - 4 q ) + 1 - (1 - 4 q ) - -------------------------------------------- 2 1/2 -1 + (1 - 4 q ) It took, .300, seconds of CPU time The first 20 terms are [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 1]} is to equal 4 2 q (q - 1) ------------------- 2 4 6 -1 + 2 q - q + q It took, .051, seconds of CPU time The first 20 terms are [1, 1, 1, 2, 4, 7, 12, 21, 37, 65, 114, 200, 351, 616, 1081, 1897, 3329, 5842, 10252] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[1, 1]} is to equal 4 1/2 8 4 1/2 2 6 -2 q + 1 - %1 + q + q %1 - q - q ------------------------------------------------- 4 6 2 1/2 1/2 8 4 1/2 -q - 2 q - q %1 + 1 - %1 + q + q %1 4 2 6 8 %1 := -q - 2 q - 2 q + 1 + q It took, .219, seconds of CPU time The first 20 terms are [1, 1, 1, 2, 4, 8, 17, 37, 82, 185, 423, 978, 2283, 5373, 12735, 30372, 72832, 175502, 424748] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [-1, 1], [0, 0], [0, 1], [1, 0], [1, 1], [0, -1], [1, -1], [-1, -1]} is to equal 4 2 1/2 10 7 1/2 6 8 1/2 4 1/2 (1 + 5 q - 3 q - 4 %1 q + q %1 + 6 q - 18 q - %2 - 2 q %1 5 1/2 6 1/2 2 1/2 9 1/2 1/2 10 - 5 q %1 + 3 q %1 + q %1 + 8 q %1 - %1 + q 6 1/2 5 1/2 2 1/2 4 1/2 9 1/2 12 + 3 q %2 + 5 q %2 + q %2 - 2 q %2 - 8 q %2 + 15 q 7 1/2 13 1/2 8 1/2 1/2 1/2 1/2 12 1/2 - q %2 + q %1 + 2 q %2 - %2 q + %1 %2 + q %2 8 1/2 1/2 1/2 6 1/2 10 1/2 1/2 10 1/2 + 5 q %1 %2 - 5 %1 q %2 - q %1 %2 - 4 q %2 8 1/2 1/2 13 1/2 11 1/2 11 1/2 12 1/2 + 2 q %1 + %1 q - q %2 - 6 q %1 + 6 q %2 + q %1 14 16 / 4 2 1/2 10 7 1/2 6 - 8 q + q ) / (2 + 10 q - 4 q - 6 %1 q - q %1 + 15 q / 8 1/2 4 1/2 5 1/2 6 1/2 3 1/2 - 34 q - 2 %2 - 4 q %1 - 12 q %1 + 5 q %1 + q %1 9 1/2 1/2 10 6 1/2 5 1/2 3 1/2 + 16 q %1 - 2 %1 - 7 q + 5 q %2 + 12 q %2 - q %2 4 1/2 9 1/2 12 7 1/2 13 1/2 8 1/2 - 4 q %2 - 16 q %2 + 27 q + q %2 + q %1 + 6 q %2 1/2 1/2 1/2 12 1/2 1/2 2 1/2 - 2 %2 q + 2 %1 %2 + q %2 + 2 %1 q %2 8 1/2 1/2 1/2 6 1/2 10 1/2 1/2 10 1/2 + 7 q %1 %2 - 11 %1 q %2 - q %1 %2 - 6 q %2 8 1/2 1/2 13 1/2 11 1/2 11 1/2 + 6 q %1 + 2 %1 q - q %2 - 8 q %1 + 8 q %2 12 1/2 14 16 + q %1 - 10 q + q ) 2 4 5 6 %1 := 1 + 2 q - q - q - 2 q + q 2 4 5 6 %2 := 1 - 2 q - q - q + 2 q + q It took, 3.020, seconds of CPU time The first 20 terms are [1, 2, 7, 28, 122, 558, 2641, 12822, 63501, 319554, 1629321, 8399092, 43701735, 229211236, 1210561517, 6432491192, 34364148528, 184463064936, 0] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[0, 0]} is to equal 4 q ------------- 2 4 1 - 2 q + q It took, .030, seconds of CPU time The first 20 terms are [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[1, 0]} is to equal 4 q - ------------ 2 4 -1 + q + q It took, .199, seconds of CPU time The first 20 terms are [1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 1], [1, 1], [1, -1], [-1, -1]} is to equal 4 2 6 8 1/2 1/2 1/2 6 1/2 1/2 (-1 - 3 q - 2 q - 6 q - 4 q - %1 %2 + q %2 + 4 q %1 %2 2 1/2 1/2 1/2 10 4 1/2 2 1/2 - 3 q %1 %2 - q %1 + 16 q + 4 q %2 + 3 q %2 3 1/2 1/2 7 1/2 1/2 8 1/2 8 1/2 + 4 q %2 + %1 - 4 q %2 + %2 - 8 q %2 - 8 q %1 7 1/2 5 1/2 5 1/2 2 1/2 4 1/2 3 1/2 + 4 q %1 - q %2 + q %1 + 3 q %1 + 4 q %1 - 4 q %1 ) / 4 2 6 8 1/2 1/2 6 1/2 / (-2 - 18 q - 6 q - 44 q - 32 q - 2 %1 %2 + 8 q %1 / 1/2 6 1/2 1/2 4 1/2 1/2 2 1/2 1/2 + 2 q %2 + 16 q %1 %2 - 4 q %1 %2 - 8 q %1 %2 1/2 10 4 1/2 2 1/2 3 1/2 1/2 - 2 q %1 + 64 q + 16 q %2 + 8 q %2 + 9 q %2 + 2 %1 7 1/2 1/2 8 1/2 6 1/2 8 1/2 - 16 q %2 + 2 %2 - 32 q %2 + 8 q %2 - 32 q %1 7 1/2 5 1/2 5 1/2 2 1/2 4 1/2 + 16 q %1 - 4 q %2 + 4 q %1 + 8 q %1 + 16 q %1 3 1/2 - 9 q %1 ) 2 3 4 %1 := 1 + 2 q + q + 4 q + 4 q 2 3 4 %2 := 1 - 2 q + q - 4 q + 4 q It took, 3.339, seconds of CPU time The first 20 terms are [1, 1, 1, 5, 14, 46, 154, 506, 1741, 6013, 21063, 74687, 266811, 961367, 3486905, 12722209, 46667911, 171988539, 0] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [-1, -1]} is to equal 4 2 2 4 1/2 2 2 4 1/2 q + 2 q - (1 - 2 q - 3 q ) q - 1 + (1 - 2 q - 3 q ) -------------------------------------------------------------- 2 2 4 1/2 q - 1 + (1 - 2 q - 3 q ) It took, .400, seconds of CPU time The first 20 terms are [1, 1, 2, 4, 9, 21, 51, 127, 323, 835, 2188, 5798, 15511, 41835, 113634, 310572, 853467, 2356779, 6536382] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[0, 0], [-1, -1]} is to equal 4 2 8 1/2 2 4 1/2 1/2 1 + q - 3 q + 2 q + %1 q + q %1 - %1 -------------------------------------------------- 4 1/2 2 1/2 6 8 2 q %1 - 2 q - %1 - 2 q + 4 q + 1 8 4 2 6 %1 := 4 q + 4 q + 1 - 4 q - 4 q It took, .389, seconds of CPU time The first 20 terms are [1, 2, 3, 5, 10, 22, 51, 123, 305, 771, 1978, 5136, 13470, 35628, 94927, 254541, 686379, 1860089, 5063333] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, 0], [-1, -1]} is to equal 1/2 8 4 1/2 2 6 2 1/2 1 - %1 + q + q %1 - 3 q + q + q %1 ------------------------------------------------ 1/2 8 4 1/2 2 1 - %1 + q + q %1 - 2 q 4 8 2 %1 := 1 + 2 q + q - 4 q It took, .400, seconds of CPU time The first 20 terms are [1, 2, 4, 9, 22, 57, 154, 429, 1223, 3550, 10455, 31160, 93802, 284789, 871008, 2681019, 8298933, 25817396, 80674902] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[0, 1], [-1, -1]} is to equal 4 2 2 4 1/2 2 2 4 1/2 q + 2 q - (1 - 2 q - 3 q ) q - 1 + (1 - 2 q - 3 q ) -------------------------------------------------------------- 2 2 4 1/2 q - 1 + (1 - 2 q - 3 q ) It took, .380, seconds of CPU time The first 20 terms are [1, 1, 2, 4, 9, 21, 51, 127, 323, 835, 2188, 5798, 15511, 41835, 113634, 310572, 853467, 2356779, 6536382] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, 1], [-1, -1]} is to equal 4 2 6 8 1/2 1/2 4 -1 + 4 q + q + q + q + %1 - %1 q - ------------------------------------------------- 1/2 4 1/2 2 1/2 4 8 6 -%1 q - %1 q - %1 + 1 - q + q + 2 q 4 2 6 8 %1 := -5 q - 2 q + 2 q + 1 + q It took, .409, seconds of CPU time The first 20 terms are [1, 1, 3, 6, 16, 40, 109, 297, 836, 2377, 6869, 20042, 59071, 175453, 524881, 1579752, 4780656, 14536878, 44394980] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[0, 0], [0, 1], [-1, -1]} is to equal 1/2 8 4 1/2 2 6 2 1/2 1 - %1 + q + q %1 - 3 q + q + q %1 ------------------------------------------------ 1/2 8 4 1/2 2 1 - %1 + q + q %1 - 2 q 4 8 2 %1 := 1 + 2 q + q - 4 q It took, .389, seconds of CPU time The first 20 terms are [1, 2, 4, 9, 22, 57, 154, 429, 1223, 3550, 10455, 31160, 93802, 284789, 871008, 2681019, 8298933, 25817396, 80674902] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, 0], [0, 1], [-1, -1]} is to equal 2 6 1/2 2 4 6 2 6 1/2 2 (1 - (1 - 4 q + 4 q ) - 3 q - q + 2 q + (1 - 4 q + 4 q ) q 2 6 1/2 4 / 2 6 1/2 2 6 + (1 - 4 q + 4 q ) q ) / (1 - (1 - 4 q + 4 q ) - 2 q + 2 q ) / It took, .570, seconds of CPU time The first 20 terms are [1, 2, 5, 13, 36, 104, 311, 955, 2995, 9553, 30896, 101082, 333946, 1112496, 3732955, 12605029, 42800317, 146046819, 500555447] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[1, 0], [-1, -1]} is to equal 4 2 4 1/2 2 2 q - 1 + (1 - 2 q - 3 q ) + q - ------------------------------------ 2 2 4 1/2 1 + q - (1 - 2 q - 3 q ) It took, .429, seconds of CPU time The first 20 terms are [1, 1, 2, 4, 9, 21, 51, 127, 323, 835, 2188, 5798, 15511, 41835, 113634, 310572, 853467, 2356779, 6536382] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [1, 0], [-1, -1]} is to equal 4 2 6 4 2 6 8 1/2 / - (-1 + 3 q + q + 2 q + (-5 q - 2 q - 2 q + 1 + q ) ) / ( / 4 2 6 8 1/2 2 2 4 6 -(-5 q - 2 q - 2 q + 1 + q ) q + 1 + 2 q + 2 q + q 4 2 6 8 1/2 - (-5 q - 2 q - 2 q + 1 + q ) ) It took, .660, seconds of CPU time The first 20 terms are [1, 1, 3, 7, 19, 53, 153, 453, 1367, 4191, 13015, 40857, 129441, 413337, 1328971, 4298727, 13978971, 45673981, 149867513] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[0, 0], [1, 0], [-1, -1]} is to equal 4 2 4 8 2 1/2 q + 2 q + (1 + 2 q + q - 4 q ) - 1 ----------------------------------------- 4 4 8 2 1/2 q - 1 + (1 + 2 q + q - 4 q ) It took, .641, seconds of CPU time The first 20 terms are [1, 2, 4, 9, 22, 57, 154, 429, 1223, 3550, 10455, 31160, 93802, 284789, 871008, 2681019, 8298933, 25817396, 80674902] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, 0], [1, 0], [-1, -1]} is to equal 2 2 2 1/2 2 1/2 -3 q + q (1 - 4 q ) + 1 - (1 - 4 q ) - -------------------------------------------- 2 1/2 -1 + (1 - 4 q ) It took, .460, seconds of CPU time The first 20 terms are [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[0, 1], [1, 0], [-1, -1]} is to equal 4 2 6 4 2 6 8 1/2 / - (-1 + 3 q + q + 2 q + (-5 q - 2 q - 2 q + 1 + q ) ) / ( / 4 2 6 8 1/2 2 2 4 6 -(-5 q - 2 q - 2 q + 1 + q ) q + 1 + 2 q + 2 q + q 4 2 6 8 1/2 - (-5 q - 2 q - 2 q + 1 + q ) ) It took, .639, seconds of CPU time The first 20 terms are [1, 1, 3, 7, 19, 53, 153, 453, 1367, 4191, 13015, 40857, 129441, 413337, 1328971, 4298727, 13978971, 45673981, 149867513] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, 1], [1, 0], [-1, -1]} is to equal 4 2 6 4 2 6 8 1/2 / - (-1 + 4 q + q + 4 q + (-7 q - 2 q - 4 q + 1 + 4 q ) ) / ( / 4 2 6 8 1/2 2 2 4 6 -2 (-7 q - 2 q - 4 q + 1 + 4 q ) q + 3 q + 4 q + 4 q 4 2 6 8 1/2 - (-7 q - 2 q - 4 q + 1 + 4 q ) + 1) It took, .531, seconds of CPU time The first 20 terms are [1, 1, 4, 10, 31, 97, 313, 1039, 3505, 12019, 41722, 146380, 518209, 1848799, 6640588, 23993602, 87149041, 318024403, 1165413340] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[0, 0], [0, 1], [1, 0], [-1, -1]} is to equal 2 1/2 2 2 2 1/2 1 - (1 - 4 q ) - 3 q + q (1 - 4 q ) - ------------------------------------------- 2 1/2 -1 + (1 - 4 q ) It took, .630, seconds of CPU time The first 20 terms are [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, 0], [0, 1], [1, 0], [-1, -1]} is to equal 4 1/2 2 6 1/2 2 -1 + q + %1 + 3 q + q - %1 q - -------------------------------------- 2 4 6 1/2 1/2 2 1 + q + q + q - %1 - %1 q 4 8 2 %1 := 1 - 2 q + q - 4 q It took, .491, seconds of CPU time The first 20 terms are [1, 2, 6, 19, 64, 225, 816, 3031, 11473, 44096, 171631, 675130, 2679728, 10719237, 43168826, 174885089, 712222799, 2914150406, 11973792218] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[1, 1], [-1, -1]} is to equal 4 1/2 8 4 1/2 2 6 -4 q + 1 - %1 + 4 q + 2 q %1 - q - 2 q 1/2 ------------------------------------------------------- 4 6 2 1/2 1/2 8 4 1/2 -3 q - 4 q - q %1 + 1 - %1 + 4 q + 2 q %1 4 2 6 8 %1 := -3 q - 2 q - 4 q + 1 + 4 q It took, .449, seconds of CPU time The first 20 terms are [1, 1, 1, 3, 7, 17, 45, 119, 323, 893, 2497, 7067, 20191, 58153, 168693, 492383, 1445051, 4261653, 12622985] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [1, 1], [-1, -1]} is to equal 4 2 6 8 1/2 4 1/2 1 - 5 q - q - 2 q + 2 q + 2 %1 q - %1 1/2 -------------------------------------------------- 1/2 4 1/2 2 4 1/2 8 6 %1 q - %1 q + 1 - 3 q - %1 + q - 2 q 4 2 6 8 %1 := -5 q - 2 q - 2 q + 1 + q It took, .650, seconds of CPU time The first 20 terms are [1, 1, 2, 5, 13, 36, 103, 303, 910, 2779, 8603, 26936, 85149, 271389, 871154, 2813849, 9138849, 29826476, 97770747] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[0, 0], [1, 1], [-1, -1]} is to equal 4 2 6 8 1/2 1/2 4 1/2 2 1 - q - 3 q + q + 6 q - %1 + 2 %1 q + %1 q 1/2 --------------------------------------------------------- 1/2 4 4 2 1/2 8 6 3 %1 q - 2 q - 2 q - %1 + 9 q - 2 q + 1 8 4 2 6 %1 := 9 q + 2 q + 1 - 4 q - 4 q It took, .470, seconds of CPU time The first 20 terms are [1, 2, 3, 6, 15, 40, 113, 332, 997, 3046, 9439, 29586, 93635, 298812, 960461, 3106648, 10104489, 33027690, 108431995] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, 0], [1, 1], [-1, -1]} is to equal 4 8 2 1/2 8 4 8 2 1/2 2 1/2 (1 - 2 q - (1 + 4 q - 4 q ) + 4 q + 2 q (1 + 4 q - 4 q ) - 3 q 6 2 8 2 1/2 / + 2 q + q (1 + 4 q - 4 q ) ) / ( / 4 8 2 1/2 8 4 8 2 1/2 2 1 - 2 q - (1 + 4 q - 4 q ) + 4 q + 2 q (1 + 4 q - 4 q ) - 2 q ) It took, .491, seconds of CPU time The first 20 terms are [1, 2, 4, 10, 28, 84, 264, 856, 2840, 9592, 32864, 113936, 398944, 1408768, 5011200, 17939648, 64583936, 233667584, 849190272] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[0, 1], [1, 1], [-1, -1]} is to equal 4 2 6 8 1/2 4 1/2 1 - 5 q - q - 2 q + 2 q + 2 %1 q - %1 1/2 -------------------------------------------------- 1/2 4 1/2 2 4 1/2 8 6 %1 q - %1 q + 1 - 3 q - %1 + q - 2 q 4 2 6 8 %1 := -5 q - 2 q - 2 q + 1 + q It took, .481, seconds of CPU time The first 20 terms are [1, 1, 2, 5, 13, 36, 103, 303, 910, 2779, 8603, 26936, 85149, 271389, 871154, 2813849, 9138849, 29826476, 97770747] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, 1], [1, 1], [-1, -1]} is to equal 4 2 6 2 4 1/2 2 4 1/2 4 -1 + 6 q + q + 2 q + (1 - 2 q - 7 q ) - 2 (1 - 2 q - 7 q ) q 1/2 ------------------------------------------------------------------------ 2 4 1/2 2 2 4 1/2 4 (1 - 2 q - 7 q ) q - 1 + (1 - 2 q - 7 q ) + 3 q It took, .470, seconds of CPU time The first 20 terms are [1, 1, 3, 7, 21, 61, 191, 603, 1961, 6457, 21595, 72975, 249085, 857013, 2970007, 10356323, 36311633, 127937649, 452738867] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[0, 0], [0, 1], [1, 1], [-1, -1]} is to equal 4 8 2 1/2 8 4 8 2 1/2 2 1/2 (1 - 2 q - (1 + 4 q - 4 q ) + 4 q + 2 q (1 + 4 q - 4 q ) - 3 q 6 2 8 2 1/2 / + 2 q + q (1 + 4 q - 4 q ) ) / ( / 4 8 2 1/2 8 4 8 2 1/2 2 1 - 2 q - (1 + 4 q - 4 q ) + 4 q + 2 q (1 + 4 q - 4 q ) - 2 q ) It took, .470, seconds of CPU time The first 20 terms are [1, 2, 4, 10, 28, 84, 264, 856, 2840, 9592, 32864, 113936, 398944, 1408768, 5011200, 17939648, 64583936, 233667584, 849190272] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, 0], [0, 1], [1, 1], [-1, -1]} is to equal 6 4 2 1/2 2 1/2 2 q + q - 4 q + 2 %1 q - %1 + 1 1/2 ----------------------------------------- 6 4 1/2 2 2 1/2 q + q + %1 q - 3 q - %1 + 1 4 8 2 6 %1 := 1 - 2 q + q - 4 q + 4 q It took, .520, seconds of CPU time The first 20 terms are [1, 2, 5, 14, 43, 140, 475, 1660, 5933, 21582, 79633, 297306, 1121015, 4262712, 16327799, 62940920, 243989945, 950539130, 3719608221] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [1, 0], [1, 1], [-1, -1]} is to equal 2 2 2 1/2 2 1/2 -3 q + q (1 - 4 q ) + 1 - (1 - 4 q ) - 1/2 -------------------------------------------- 2 1/2 2 -1 + (1 - 4 q ) + q It took, .650, seconds of CPU time The first 20 terms are [1, 1, 3, 8, 24, 75, 243, 808, 2742, 9458, 33062, 116868, 417022, 1500159, 5434563, 19808976, 72596742, 267343374, 988779258] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, 0], [1, 0], [1, 1], [-1, -1]} is to equal 2 6 1/2 2 4 1/2 8 4 1/2 -3 q + q + %1 q + 1 - 2 q - %1 + q + q %1 -------------------------------------------------------- 4 1/2 8 4 1/2 2 2 - 3 q - 2 %1 + q + q %1 - 2 q 4 8 2 %1 := 1 - 2 q + q - 4 q It took, .511, seconds of CPU time The first 20 terms are [1, 2, 5, 15, 49, 169, 605, 2226, 8365, 31967, 123847, 485304, 1920081, 7659523, 30773793, 124413854, 505760871, 2066067038, 8477004831] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[0, 1], [1, 0], [1, 1], [-1, -1]} is to equal 2 1/2 2 2 2 1/2 1 - (1 - 4 q ) - 3 q + q (1 - 4 q ) - 1/2 ------------------------------------------- 2 1/2 2 -1 + (1 - 4 q ) + q It took, .650, seconds of CPU time The first 20 terms are [1, 1, 3, 8, 24, 75, 243, 808, 2742, 9458, 33062, 116868, 417022, 1500159, 5434563, 19808976, 72596742, 267343374, 988779258] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, 1], [1, 0], [1, 1], [-1, -1]} is to equal 6 4 2 1/2 2 1/2 q + 4 q + 2 q - %1 q - 1 + %1 - --------------------------------------- 6 4 2 1/2 2 1/2 q - q + q - %1 q + 2 - 2 %1 4 2 6 8 %1 := -9 q - 2 q - 6 q + 1 + q It took, .551, seconds of CPU time The first 20 terms are [1, 1, 4, 11, 37, 126, 447, 1625, 6026, 22709, 86705, 334708, 1304149, 5122265, 20258712, 80612887, 322501997, 1296399730, 5233683579] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[0, 0], [0, 1], [1, 0], [1, 1], [-1, -1]} is to equal 4 1/2 8 4 1/2 2 6 1/2 2 1 - 2 q - %1 + q + q %1 - 3 q + q + %1 q ------------------------------------------------------- 4 1/2 8 4 1/2 2 2 - 3 q - 2 %1 + q + q %1 - 2 q 4 8 2 %1 := 1 - 2 q + q - 4 q It took, .500, seconds of CPU time The first 20 terms are [1, 2, 5, 15, 49, 169, 605, 2226, 8365, 31967, 123847, 485304, 1920081, 7659523, 30773793, 124413854, 505760871, 2066067038, 8477004831] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, 0], [0, 1], [1, 0], [1, 1], [-1, -1]} is to equal 2 4 1/2 2 4 2 4 1/2 2 - (1 - (1 - 4 q - 4 q ) - 3 q - 3 q + (1 - 4 q - 4 q ) q 2 4 1/2 4 / + (1 - 4 q - 4 q ) q ) / ( / 2 4 1/2 2 4 2 4 1/2 2 -2 + 2 (1 - 4 q - 4 q ) + q + 2 q + (1 - 4 q - 4 q ) q ) It took, .690, seconds of CPU time The first 20 terms are [1, 2, 6, 20, 72, 272, 1064, 4272, 17504, 72896, 307648, 1312896, 5655808, 24562176, 107419264, 472675072, 2091206144, 9296612352, 41507566592] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[0, -1], [-1, -1]} is to equal 2 4 1/2 4 2 -1 + (1 - 2 q - 3 q ) + 2 q + q - ------------------------------------- 2 2 4 1/2 1 + q - (1 - 2 q - 3 q ) It took, .400, seconds of CPU time The first 20 terms are [1, 1, 2, 4, 9, 21, 51, 127, 323, 835, 2188, 5798, 15511, 41835, 113634, 310572, 853467, 2356779, 6536382] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, -1], [-1, -1]} is to equal 4 2 6 4 2 6 8 1/2 / - (-1 + 3 q + q + 2 q + (-5 q - 2 q - 2 q + 1 + q ) ) / ( / 4 2 6 8 1/2 2 2 4 6 -(-5 q - 2 q - 2 q + 1 + q ) q + 1 + 2 q + 2 q + q 4 2 6 8 1/2 - (-5 q - 2 q - 2 q + 1 + q ) ) It took, .440, seconds of CPU time The first 20 terms are [1, 1, 3, 7, 19, 53, 153, 453, 1367, 4191, 13015, 40857, 129441, 413337, 1328971, 4298727, 13978971, 45673981, 149867513] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[0, 0], [0, -1], [-1, -1]} is to equal 4 2 4 8 2 1/2 q + 2 q + (1 + 2 q + q - 4 q ) - 1 ----------------------------------------- 4 4 8 2 1/2 q - 1 + (1 + 2 q + q - 4 q ) It took, .431, seconds of CPU time The first 20 terms are [1, 2, 4, 9, 22, 57, 154, 429, 1223, 3550, 10455, 31160, 93802, 284789, 871008, 2681019, 8298933, 25817396, 80674902] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[0, 1], [0, -1], [-1, -1]} is to equal 4 2 6 4 2 6 8 1/2 / - (-1 + 3 q + q + 2 q + (-5 q - 2 q - 2 q + 1 + q ) ) / ( / 4 2 6 8 1/2 2 2 4 6 -(-5 q - 2 q - 2 q + 1 + q ) q + 1 + 2 q + 2 q + q 4 2 6 8 1/2 - (-5 q - 2 q - 2 q + 1 + q ) ) It took, .451, seconds of CPU time The first 20 terms are [1, 1, 3, 7, 19, 53, 153, 453, 1367, 4191, 13015, 40857, 129441, 413337, 1328971, 4298727, 13978971, 45673981, 149867513] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, 1], [0, -1], [-1, -1]} is to equal 4 2 6 4 2 6 8 1/2 / - (-1 + 4 q + q + 4 q + (-7 q - 2 q - 4 q + 1 + 4 q ) ) / ( / 4 2 6 8 1/2 2 2 4 6 -2 (-7 q - 2 q - 4 q + 1 + 4 q ) q + 3 q + 4 q + 4 q 4 2 6 8 1/2 - (-7 q - 2 q - 4 q + 1 + 4 q ) + 1) It took, .459, seconds of CPU time The first 20 terms are [1, 1, 4, 10, 31, 97, 313, 1039, 3505, 12019, 41722, 146380, 518209, 1848799, 6640588, 23993602, 87149041, 318024403, 1165413340] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[0, 0], [0, 1], [0, -1], [-1, -1]} is to equal 2 1/2 2 2 2 1/2 1 - (1 - 4 q ) - 3 q + q (1 - 4 q ) - ------------------------------------------- 2 1/2 -1 + (1 - 4 q ) It took, .421, seconds of CPU time The first 20 terms are [1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, 0], [0, 1], [0, -1], [-1, -1]} is to equal 4 1/2 2 6 1/2 2 -1 + q + %1 + 3 q + q - %1 q - -------------------------------------- 2 4 6 1/2 1/2 2 1 + q + q + q - %1 - %1 q 4 8 2 %1 := 1 - 2 q + q - 4 q It took, .460, seconds of CPU time The first 20 terms are [1, 2, 6, 19, 64, 225, 816, 3031, 11473, 44096, 171631, 675130, 2679728, 10719237, 43168826, 174885089, 712222799, 2914150406, 11973792218] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[1, 0], [0, -1], [-1, -1]} is to equal 4 2 6 8 1/2 4 1/2 1 - 2 q - q + q + q - %1 q - %1 - ---------------------------------------------------------- 4 2 6 8 1/2 4 1/2 2 1/2 -3 q - 2 q + 2 q - 1 + q - %1 q - %1 q + %1 4 2 6 8 %1 := -5 q - 2 q + 2 q + 1 + q It took, .669, seconds of CPU time The first 20 terms are [1, 1, 3, 6, 16, 40, 109, 297, 836, 2377, 6869, 20042, 59071, 175453, 524881, 1579752, 4780656, 14536878, 44394980] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [1, 0], [0, -1], [-1, -1]} is to equal 4 2 6 8 4 1/2 1/2 1 - 3 q - q - 3 q + 2 q - q %1 - %1 - -------------------------------------------------------------- 4 1/2 1/2 2 4 2 1/2 8 6 -2 q %1 + %1 q - 1 - 7 q - 4 q + %1 + 4 q - 4 q 4 2 6 8 %1 := -7 q - 2 q - 4 q + 1 + 4 q It took, .551, seconds of CPU time The first 20 terms are [1, 1, 4, 10, 31, 97, 313, 1039, 3505, 12019, 41722, 146380, 518209, 1848799, 6640588, 23993602, 87149041, 318024403, 1165413340] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[0, 0], [1, 0], [0, -1], [-1, -1]} is to equal 2 6 1/2 2 4 6 2 6 1/2 2 - (1 - (1 - 4 q + 4 q ) - 3 q + q + 2 q + (1 - 4 q + 4 q ) q 2 6 1/2 4 / - (1 - 4 q + 4 q ) q ) / ( / 2 6 1/2 2 6 1/2 2 6 -1 + (1 - 4 q + 4 q ) - 2 (1 - 4 q + 4 q ) q + 2 q ) It took, .690, seconds of CPU time The first 20 terms are [1, 2, 5, 13, 36, 104, 311, 955, 2995, 9553, 30896, 101082, 333946, 1112496, 3732955, 12605029, 42800317, 146046819, 500555447] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, 0], [1, 0], [0, -1], [-1, -1]} is to equal 1/2 8 4 1/2 2 6 1/2 2 1 - %1 + q - q %1 - 3 q - q + %1 q - ------------------------------------------------ 4 1/2 8 4 1/2 2 -1 - 2 q + %1 + q - q %1 - 2 q 4 8 2 %1 := 1 - 2 q + q - 4 q It took, .519, seconds of CPU time The first 20 terms are [1, 2, 6, 19, 64, 225, 816, 3031, 11473, 44096, 171631, 675130, 2679728, 10719237, 43168826, 174885089, 712222799, 2914150406, 11973792218] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[0, 1], [1, 0], [0, -1], [-1, -1]} is to equal 4 2 6 8 4 1/2 1/2 1 - 3 q - q - 3 q + 2 q - q %1 - %1 - -------------------------------------------------------------- 4 1/2 1/2 2 4 2 1/2 8 6 -2 q %1 + %1 q - 1 - 7 q - 4 q + %1 + 4 q - 4 q 4 2 6 8 %1 := -7 q - 2 q - 4 q + 1 + 4 q It took, .731, seconds of CPU time The first 20 terms are [1, 1, 4, 10, 31, 97, 313, 1039, 3505, 12019, 41722, 146380, 518209, 1848799, 6640588, 23993602, 87149041, 318024403, 1165413340] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, 1], [1, 0], [0, -1], [-1, -1]} is to equal 4 2 6 8 1/2 1/2 4 1 - 4 q - q - 7 q + 3 q - %1 - %1 q - ------------------------------------------------------------------ 1/2 4 1/2 2 4 2 1/2 8 6 -3 %1 q + 3 %1 q - 11 q - 6 q + %1 + 9 q - 14 q - 1 4 2 6 8 %1 := -9 q - 2 q - 10 q + 1 + 9 q It took, .741, seconds of CPU time The first 20 terms are [1, 1, 5, 14, 48, 172, 617, 2309, 8734, 33593, 130835, 514650, 2042947, 8170917, 32898811, 133238288, 542404588, 2218324410, 9110173436] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[0, 0], [0, 1], [1, 0], [0, -1], [-1, -1]} is to equal 1/2 8 4 1/2 2 6 1/2 2 1 - %1 + q - q %1 - 3 q - q + %1 q - ------------------------------------------------ 4 1/2 8 4 1/2 2 -1 - 2 q + %1 + q - q %1 - 2 q 4 8 2 %1 := 1 - 2 q + q - 4 q It took, .521, seconds of CPU time The first 20 terms are [1, 2, 6, 19, 64, 225, 816, 3031, 11473, 44096, 171631, 675130, 2679728, 10719237, 43168826, 174885089, 712222799, 2914150406, 11973792218] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, 0], [0, 1], [1, 0], [0, -1], [-1, -1]} is to equal 4 2 6 8 1/2 1/2 2 4 1/2 1 - q - 3 q - 4 q + 2 q - %1 + %1 q - q %1 - ---------------------------------------------------------------- 4 2 4 1/2 1/2 2 6 8 1/2 -1 - 4 q - 4 q - 2 q %1 + 2 %1 q - 6 q + 4 q + %1 8 4 2 6 %1 := 4 q - 4 q + 1 - 4 q - 4 q It took, .560, seconds of CPU time The first 20 terms are [1, 2, 7, 25, 94, 370, 1499, 6215, 26245, 112483, 488046, 2139540, 9462486, 42168756, 189170439, 853582641, 3871504639, 17640644953, 80713308161] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[0, 1], [1, 1], [0, -1], [-1, -1]} is to equal 2 1/2 2 2 2 1/2 1 - (1 - 4 q ) - 3 q + q (1 - 4 q ) - 1/2 ------------------------------------------- 2 1/2 2 -1 + (1 - 4 q ) + q It took, .699, seconds of CPU time The first 20 terms are [1, 1, 3, 8, 24, 75, 243, 808, 2742, 9458, 33062, 116868, 417022, 1500159, 5434563, 19808976, 72596742, 267343374, 988779258] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, 1], [1, 1], [0, -1], [-1, -1]} is to equal 6 4 2 1/2 2 1/2 q + 4 q + 2 q - %1 q - 1 + %1 - --------------------------------------- 6 4 2 1/2 2 1/2 q - q + q - %1 q + 2 - 2 %1 4 2 6 8 %1 := -9 q - 2 q - 6 q + 1 + q It took, .560, seconds of CPU time The first 20 terms are [1, 1, 4, 11, 37, 126, 447, 1625, 6026, 22709, 86705, 334708, 1304149, 5122265, 20258712, 80612887, 322501997, 1296399730, 5233683579] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[0, 0], [0, 1], [1, 1], [0, -1], [-1, -1]} is to equal 4 1/2 8 4 1/2 2 6 1/2 2 1 - 2 q - %1 + q + q %1 - 3 q + q + %1 q ------------------------------------------------------- 4 1/2 8 4 1/2 2 2 - 3 q - 2 %1 + q + q %1 - 2 q 4 8 2 %1 := 1 - 2 q + q - 4 q It took, .701, seconds of CPU time The first 20 terms are [1, 2, 5, 15, 49, 169, 605, 2226, 8365, 31967, 123847, 485304, 1920081, 7659523, 30773793, 124413854, 505760871, 2066067038, 8477004831] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, 0], [0, 1], [1, 1], [0, -1], [-1, -1]} is to equal 2 4 1/2 2 4 2 4 1/2 2 - (1 - (1 - 4 q - 4 q ) - 3 q - 3 q + (1 - 4 q - 4 q ) q 2 4 1/2 4 / + (1 - 4 q - 4 q ) q ) / ( / 2 4 1/2 2 4 2 4 1/2 2 -2 + 2 (1 - 4 q - 4 q ) + q + 2 q + (1 - 4 q - 4 q ) q ) It took, .530, seconds of CPU time The first 20 terms are [1, 2, 6, 20, 72, 272, 1064, 4272, 17504, 72896, 307648, 1312896, 5655808, 24562176, 107419264, 472675072, 2091206144, 9296612352, 41507566592] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, 1], [1, 0], [1, 1], [0, -1], [-1, -1]} is to equal 4 2 6 4 2 6 8 1/2 / - 1/2 (-1 + 6 q + q + 8 q + (-11 q - 2 q - 12 q + 1 + 4 q ) ) / ( / 4 2 6 8 1/2 2 2 4 -2 (-11 q - 2 q - 12 q + 1 + 4 q ) q + 1 + 3 q + 4 q 4 2 6 8 1/2 6 - (-11 q - 2 q - 12 q + 1 + 4 q ) + 4 q ) It took, .551, seconds of CPU time The first 20 terms are [1, 1, 5, 15, 55, 209, 809, 3243, 13195, 54613, 228901, 969783, 4146687, 17870489, 77544513, 338511523, 1485606387, 6550728349, 29008005309] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, 0], [0, 1], [1, 0], [1, 1], [0, -1], [-1, -1]} is to equal 4 1/2 2 6 1/2 2 -1 + 3 q + %1 + 3 q + 3 q - %1 q - 1/2 ------------------------------------------ 2 4 6 1/2 1/2 2 1 + q + q + q - %1 - %1 q 4 8 2 6 %1 := 1 - 6 q + q - 4 q - 4 q It took, .750, seconds of CPU time The first 20 terms are [1, 2, 7, 26, 103, 428, 1837, 8084, 36277, 165374, 763699, 3565166, 16796971, 79765688, 381404185, 1834730216, 8873058505, 43115712602, 210399660703] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [-1, 1]} is to equal 4 2 q (-1 + q ) ------------ 2 -1 + 2 q It took, .271, seconds of CPU time The first 20 terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, 0]} is to equal 4 q - --------- 2 -1 + 2 q It took, .060, seconds of CPU time The first 20 terms are [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 1], [0, 0]} is to equal 4 2 q (-1 + q ) ----------------------- 2 4 6 -1 + 3 q - 3 q + 2 q It took, .070, seconds of CPU time The first 20 terms are [1, 2, 3, 5, 10, 21, 43, 86, 171, 341, 682, 1365, 2731, 5462, 10923, 21845, 43690, 87381, 174763] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [-1, 1], [0, 0]} is to equal 4 2 q (-1 + q ) --------------------- 2 4 6 -1 + 3 q - 2 q + q It took, .270, seconds of CPU time The first 20 terms are [1, 2, 4, 9, 21, 49, 114, 265, 616, 1432, 3329, 7739, 17991, 41824, 97229, 226030, 525456, 1221537, 2839729] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[0, 1]} is to equal 4 q - ------------ 2 4 -1 + q + q It took, .050, seconds of CPU time The first 20 terms are [1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, 1]} is to equal 4 q - -------------- 2 4 -1 + q + 2 q It took, .049, seconds of CPU time The first 20 terms are [1, 1, 3, 5, 11, 21, 43, 85, 171, 341, 683, 1365, 2731, 5461, 10923, 21845, 43691, 87381, 174763] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 1], [0, 1]} is to equal 4 2 q (-1 + q ) ------------ 2 -1 + 2 q It took, .070, seconds of CPU time The first 20 terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [-1, 1], [0, 1]} is to equal 4 2 q (q - 1) - ------------------ 2 4 6 1 - 2 q - q + q It took, .280, seconds of CPU time The first 20 terms are [1, 1, 3, 6, 14, 31, 70, 157, 353, 793, 1782, 4004, 8997, 20216, 45425, 102069, 229347, 515338, 1157954] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[0, 0], [0, 1]} is to equal 4 q - --------- 2 -1 + 2 q It took, .051, seconds of CPU time The first 20 terms are [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, 0], [0, 1]} is to equal 4 q - -------------- 2 4 -1 + 2 q + q It took, .060, seconds of CPU time The first 20 terms are [1, 2, 5, 12, 29, 70, 169, 408, 985, 2378, 5741, 13860, 33461, 80782, 195025, 470832, 1136689, 2744210, 6625109] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 1], [0, 0], [0, 1]} is to equal 4 2 q (q - 1) --------------------- 2 4 6 -1 + 3 q - 2 q + q It took, .280, seconds of CPU time The first 20 terms are [1, 2, 4, 9, 21, 49, 114, 265, 616, 1432, 3329, 7739, 17991, 41824, 97229, 226030, 525456, 1221537, 2839729] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [1, 0]} is to equal 4 2 6 8 4 2 8 1/2 - 1/2 (1 - q - q - q + 2 q - (-3 q - 2 q + 1 + 4 q ) 4 4 2 8 1/2 / 2 - q (-3 q - 2 q + 1 + 4 q ) ) / (q / 4 2 8 1/2 2 2 6 (-(-3 q - 2 q + 1 + 4 q ) q - 1 - q + 2 q )) It took, .421, seconds of CPU time The first 20 terms are [1, 1, 3, 6, 14, 33, 79, 194, 482, 1214, 3090, 7936, 20544, 53545, 140399, 370098, 980226, 2607242, 6961462] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, 0], [1, 0]} is to equal 2 6 1/2 2 4 1/2 8 4 1/2 -3 q - q + %1 q + 1 + 2 q - %1 + q - q %1 - -------------------------------------------------------- 2 6 1/2 2 2 q (q - %1 q + q - 2) 4 8 2 %1 := 1 + 2 q + q - 4 q It took, .391, seconds of CPU time The first 20 terms are [1, 2, 5, 13, 35, 97, 275, 794, 2327, 6905, 20705, 62642, 190987, 586219, 1810011, 5617914, 17518463, 54857506, 172431935] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[0, 1], [1, 0]} is to equal 4 2 6 8 4 4 2 8 1/2 - 1/2 (1 - q - q - q + 2 q - q (-3 q - 2 q + 1 + 4 q ) 4 2 8 1/2 / 2 - (-3 q - 2 q + 1 + 4 q ) ) / (q / 4 2 8 1/2 2 2 6 (-(-3 q - 2 q + 1 + 4 q ) q - 1 - q + 2 q )) It took, .419, seconds of CPU time The first 20 terms are [1, 1, 3, 6, 14, 33, 79, 194, 482, 1214, 3090, 7936, 20544, 53545, 140399, 370098, 980226, 2607242, 6961462] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, 1], [1, 0]} is to equal 4 2 6 8 1/2 1/2 4 1 - 2 q - q - 3 q + 3 q - %1 - %1 q - ------------------------------------------------- 2 2 1/2 2 1/2 4 6 q (-4 q - 3 - 3 %1 q + %1 - 4 q + 9 q ) 4 2 6 8 %1 := -5 q - 2 q - 2 q + 1 + 9 q It took, .439, seconds of CPU time The first 20 terms are [1, 1, 4, 9, 25, 70, 197, 575, 1690, 5045, 15223, 46340, 142241, 439573, 1366768, 4272617, 13420445, 42335626, 134067245] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[0, 0], [0, 1], [1, 0]} is to equal 2 6 1/2 2 4 1/2 8 4 1/2 -3 q - q + %1 q + 1 + 2 q - %1 + q - q %1 - -------------------------------------------------------- 2 6 1/2 2 2 q (q - %1 q + q - 2) 4 8 2 %1 := 1 + 2 q + q - 4 q It took, .389, seconds of CPU time The first 20 terms are [1, 2, 5, 13, 35, 97, 275, 794, 2327, 6905, 20705, 62642, 190987, 586219, 1810011, 5617914, 17518463, 54857506, 172431935] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, 0], [0, 1], [1, 0]} is to equal 4 2 6 8 4 8 2 1/2 - (1 + q - 3 q - 2 q + 2 q - q (1 + 4 q - 4 q ) 8 2 1/2 2 8 2 1/2 / 2 + (1 + 4 q - 4 q ) q - (1 + 4 q - 4 q ) ) / (q / 8 2 1/2 2 8 2 1/2 6 4 (-2 (1 + 4 q - 4 q ) q + (1 + 4 q - 4 q ) - 3 + 4 q - 2 q )) It took, .431, seconds of CPU time The first 20 terms are [1, 2, 6, 18, 56, 180, 592, 1984, 6752, 23272, 81072, 285008, 1009824, 3602432, 12928448, 46644288, 169083648, 615522688, 2249288704] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[0, 1], [0, -1]} is to equal 4 2 6 8 4 4 2 8 1/2 - 1/2 (1 - q - q - q + 2 q - q (-3 q - 2 q + 1 + 4 q ) 4 2 8 1/2 / 2 - (-3 q - 2 q + 1 + 4 q ) ) / (q / 4 2 8 1/2 2 2 6 (-(-3 q - 2 q + 1 + 4 q ) q - 1 - q + 2 q )) It took, .231, seconds of CPU time The first 20 terms are [1, 1, 3, 6, 14, 33, 79, 194, 482, 1214, 3090, 7936, 20544, 53545, 140399, 370098, 980226, 2607242, 6961462] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, 1], [0, -1]} is to equal 4 2 6 8 1/2 1/2 4 1 - 2 q - q - 3 q + 3 q - %1 - %1 q - ------------------------------------------------- 2 2 1/2 2 1/2 4 6 q (-4 q - 3 - 3 %1 q + %1 - 4 q + 9 q ) 4 2 6 8 %1 := -5 q - 2 q - 2 q + 1 + 9 q It took, .440, seconds of CPU time The first 20 terms are [1, 1, 4, 9, 25, 70, 197, 575, 1690, 5045, 15223, 46340, 142241, 439573, 1366768, 4272617, 13420445, 42335626, 134067245] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[0, 0], [0, 1], [0, -1]} is to equal 4 1/2 8 4 1/2 2 6 1/2 2 1 + 2 q - %1 + q - q %1 - 3 q - q + %1 q - ------------------------------------------------------- 2 6 1/2 2 2 q (q - %1 q + q - 2) 4 8 2 %1 := 1 + 2 q + q - 4 q It took, .421, seconds of CPU time The first 20 terms are [1, 2, 5, 13, 35, 97, 275, 794, 2327, 6905, 20705, 62642, 190987, 586219, 1810011, 5617914, 17518463, 54857506, 172431935] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, 0], [0, 1], [0, -1]} is to equal 4 2 6 8 4 8 2 1/2 - (1 + q - 3 q - 2 q + 2 q - q (1 + 4 q - 4 q ) 8 2 1/2 2 8 2 1/2 / 2 + (1 + 4 q - 4 q ) q - (1 + 4 q - 4 q ) ) / (q / 8 2 1/2 2 8 2 1/2 6 4 (-2 (1 + 4 q - 4 q ) q + (1 + 4 q - 4 q ) - 3 + 4 q - 2 q )) It took, .441, seconds of CPU time The first 20 terms are [1, 2, 6, 18, 56, 180, 592, 1984, 6752, 23272, 81072, 285008, 1009824, 3602432, 12928448, 46644288, 169083648, 615522688, 2249288704] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, 1], [1, 0], [0, -1]} is to equal 4 2 6 8 4 1/2 1/2 1 - 2 q - q - 6 q + 8 q - 2 q %1 - %1 - 1/2 ------------------------------------------------- 2 1/2 1/2 2 2 6 4 q (%1 - 4 %1 q - 3 - 5 q + 16 q - 8 q ) 4 2 6 8 %1 := -7 q - 2 q - 8 q + 1 + 16 q It took, .720, seconds of CPU time The first 20 terms are [1, 1, 5, 13, 41, 137, 445, 1525, 5249, 18321, 64821, 231069, 831129, 3010137, 10968429, 40189957, 147969137, 547163873, 2031245413] The generating function for Column-Convex Polyominoes according to perimeter, where the interfaces are restricted to lie in {[-1, 0], [0, 0], [0, 1], [1, 0], [0, -1]} is to equal 4 2 6 8 1/2 1/2 2 1/2 4 1 + q - 3 q - 5 q + 6 q - %1 + %1 q - 2 %1 q - 1/2 ----------------------------------------------------------- 2 1/2 2 1/2 2 6 4 q (-3 %1 q + %1 - 3 - q + 9 q - 5 q ) 4 8 2 6 %1 := 1 - 2 q + 9 q - 4 q - 4 q It took, .741, seconds of CPU time The first 20 terms are [1, 2, 7, 24, 85, 314, 1187, 4576, 17929, 71170, 285631, 1157080, 4724957, 19429082, 80381083, 334344832, 1397389457, 5865505346, 24715750007] I succeeded in , 81, cases and failed in, 190, cases Everything took, 223.330, seconds of CPU time