The Generating Functions for 2D (2D site) Lattice-Animals of (Locally) Bounded Width The generating function (in the variable s) enumerating 2D (site) lattice animals of width <= 1 equals s - ------ -1 + s The generating function (in the variable s) enumerating 2D (site) lattice animals of width <= 2 equals s - ------------ 2 s + 2 s - 1 The generating function (in the variable s) enumerating 2D (site) lattice animals of width <= 3 equals 3 2 4 7 9 6 8 s (-1 - s + 2 s + s - s - 2 s + s - s - 2 s ) - --------------------------------------------------------------- 8 7 6 5 4 3 2 2 (s - 6 s - 7 s + 4 s + 9 s - 3 s - 6 s - s + 1) (s + 1) The generating function (in the variable s) enumerating 2D (site) lattice animals of width <= 4 equals 10 3 2 17 16 19 18 20 - s (-1 + s + 15 s + 4 s + 2 s - 3 s + 19 s + 2 s - 13 s + 4 s 12 15 13 14 5 4 7 9 6 - 32 s + 6 s - 23 s - 2 s - 9 s - 8 s - 6 s - 2 s + 6 s 8 11 / 22 21 20 19 18 17 16 + 6 s + 18 s ) / (s + 8 s - 3 s - 32 s + 5 s + 49 s - s / 15 14 13 12 11 10 8 7 - 37 s - 77 s - 46 s + 76 s + 35 s - 7 s - 22 s + 3 s 6 4 3 2 - 28 s + 17 s - s - 2 s - 3 s + 1) The generating function (in the variable s) enumerating 2D (site) lattice animals of width <= 5 equals 30 29 27 10 24 28 - s (1 - s - 83333 s - 10736 s + 66988 s + 75 s - 29310 s + 55635 s 3 2 35 23 36 61 17 - 12 s - 4 s + 107940 s - 16755 s - 546 s - 24 s - 3254 s 16 19 22 21 18 20 - 569 s - 1151 s + 3804 s + 12384 s - 4454 s + 7443 s 37 38 39 12 15 55 - 103863 s - 120274 s - 55191 s + 588 s + 426 s - 437 s 54 53 52 51 50 49 - 1486 s - 1992 s + 1738 s + 9333 s + 11266 s + 1305 s 48 13 33 34 14 47 - 11229 s + 404 s + 58818 s + 131918 s + 449 s - 16300 s 46 45 44 43 42 41 - 20569 s - 28786 s - 19063 s + 23203 s + 72377 s + 81377 s 40 5 31 4 7 9 6 8 + 31578 s + 61 s - 102758 s + 9 s - 73 s - 278 s + 84 s - 262 s 11 58 59 60 57 25 62 + 419 s + 132 s + 8 s - 12 s + 222 s - 13045 s + s 32 63 64 26 56 / 30 - 43718 s - 8 s + s + 31030 s + 44 s ) / (-1 + 3 s + 143008 s / 29 27 10 24 28 3 2 + 217416 s - 21364 s - 998 s + 5574 s + 125073 s + 5 s + 4 s 35 23 36 61 17 16 + 226135 s + 50347 s + 362009 s - 5 s + 5372 s + 4292 s 19 22 21 18 20 37 - 17300 s + 35666 s - 3185 s - 2820 s - 23969 s + 212806 s 38 39 12 15 55 54 - 90175 s - 290001 s + 8 s + 1853 s - 3190 s - 208 s 53 52 51 50 49 48 + 13000 s + 27207 s + 17358 s - 19151 s - 47708 s - 49251 s 13 33 34 14 47 46 + 1078 s - 280558 s - 70839 s + 1128 s - 48126 s - 46846 s 45 44 43 42 41 + 10157 s + 128218 s + 205680 s + 134551 s - 65676 s 40 5 31 4 7 9 6 - 261330 s - 67 s - 69476 s - 37 s + 318 s - 220 s + 27 s 8 11 58 59 60 57 25 + 303 s - 892 s + 253 s + 338 s + 95 s - 600 s - 70934 s 65 62 32 63 64 26 56 + s - 52 s - 266893 s - 5 s - 17 s - 100572 s - 1937 s )