Given sets A and B of affine linear expressions in the variable r, we inter\ ested in counting the number of Dyck paths whose ascending run-lengths are never in the range of A and descending run-l\ enths are never in the range of B Below we give the quadratic equations satisfied by the generating function f\ or all sets A and B that are subsets of {2 r + 1, 2 r + 2} ---------------------------- (A,B)= , {}, {} 2 P x - P + 1 = 0 ---------------------------- (A,B)= , {}, {2 r + 1} 3 2 P x - P + 1 = 0 ---------------------------- (A,B)= , {}, {2 r + 2} 3 2 2 2 P x - P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {}, {2 r + 1, 2 r + 2} P - 1 = 0 ---------------------------- (A,B)= , {2 r + 1}, {} 3 2 P x - P + 1 = 0 ---------------------------- (A,B)= , {2 r + 1}, {2 r + 1} 2 2 P x - P + 1 = 0 ---------------------------- (A,B)= , {2 r + 1}, {2 r + 2} 6 6 5 6 5 4 4 4 3 4 3 2 2 2 2 P x - P x - P x - P x + 3 P x + 2 P x - P x - P x - P + 1 = 0 ---------------------------- (A,B)= , {2 r + 1}, {2 r + 1, 2 r + 2} P - 1 = 0 ---------------------------- (A,B)= , {2 r + 2}, {} 3 2 2 2 P x - P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {2 r + 2}, {2 r + 1} 6 6 5 6 5 4 4 4 3 4 3 2 2 2 2 P x - P x - P x - P x + 3 P x + 2 P x - P x - P x - P + 1 = 0 ---------------------------- (A,B)= , {2 r + 2}, {2 r + 2} 2 2 2 P x - P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {2 r + 2}, {2 r + 1, 2 r + 2} P - 1 = 0 ---------------------------- (A,B)= , {2 r + 1, 2 r + 2}, {} P - 1 = 0 ---------------------------- (A,B)= , {2 r + 1, 2 r + 2}, {2 r + 1} P - 1 = 0 ---------------------------- (A,B)= , {2 r + 1, 2 r + 2}, {2 r + 2} P - 1 = 0 ---------------------------- (A,B)= , {2 r + 1, 2 r + 2}, {2 r + 1, 2 r + 2} P - 1 = 0 Below we give the quadratic equations satisfied by the generating function f\ or all sets A and B that are subsets of {3 r + 1, 3 r + 2, 3 r + 3} ---------------------------- (A,B)= , {}, {} 2 P x - P + 1 = 0 ---------------------------- (A,B)= , {}, {3 r + 1} 4 3 2 2 P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {}, {3 r + 2} 4 3 P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {}, {3 r + 3} 4 3 3 3 2 2 P x - P x + P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {}, {3 r + 1, 3 r + 2} 4 3 P x - P + 1 = 0 ---------------------------- (A,B)= , {}, {3 r + 1, 3 r + 3} 4 3 3 3 2 2 P x - P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {}, {3 r + 2, 3 r + 3} 4 3 3 3 P x - P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {}, {3 r + 1, 3 r + 2, 3 r + 3} P - 1 = 0 ---------------------------- (A,B)= , {3 r + 1}, {} 4 3 2 2 P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 1}, {3 r + 1} 8 12 7 11 6 11 7 9 6 10 6 9 5 9 5 8 5 7 P x + P x + P x - P x - 2 P x + P x - 2 P x + P x + 2 P x 4 8 5 6 4 7 4 5 3 6 3 5 4 3 3 4 + 2 P x - P x - 3 P x - 2 P x - 2 P x + P x + P x + 2 P x 2 5 3 3 2 4 2 3 2 + P x - P x - 2 P x + P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 1}, {3 r + 2} 20 30 19 27 18 28 18 27 17 28 17 26 16 27 16 26 P x - P x + P x + P x + P x - P x + P x + P x 17 24 16 25 16 24 15 25 16 23 15 24 - 3 P x - P x + P x + 3 P x + 3 P x + 3 P x 15 23 14 24 16 21 15 22 14 23 15 21 - 2 P x + 2 P x + 3 P x + P x + 5 P x - 3 P x 14 22 14 21 13 22 14 20 13 21 13 20 - 7 P x + 4 P x - P x + 2 P x + 6 P x - 7 P x 12 21 14 18 13 19 12 20 13 18 12 19 - 3 P x + 3 P x + 5 P x + 4 P x - 2 P x - 3 P x 11 20 13 17 12 18 11 19 12 17 11 18 + P x - 3 P x + 2 P x - 11 P x + 6 P x + 11 P x 10 19 13 15 12 16 11 17 10 18 12 15 + P x - 3 P x - 2 P x - 10 P x - 7 P x + 3 P x 11 16 10 17 11 15 10 16 9 17 11 14 + 10 P x - 4 P x - 6 P x + 4 P x + P x - P x 10 15 9 16 10 14 9 15 11 12 10 13 - 10 P x - 11 P x + 12 P x + 11 P x - P x - 4 P x 9 14 8 15 10 12 9 13 8 14 9 12 - 10 P x - 3 P x + 6 P x + 10 P x + 4 P x - 6 P x 8 13 9 11 8 12 7 13 10 9 8 11 7 12 - 3 P x - P x + 2 P x - P x + P x + 6 P x + 6 P x 9 9 8 10 7 11 6 12 8 9 7 10 6 11 - P x - 2 P x - 7 P x + 2 P x + 3 P x + 5 P x + 5 P x 7 9 6 10 7 8 6 9 5 10 6 8 5 9 - 2 P x - 7 P x - 3 P x + 4 P x + 3 P x + 2 P x + 3 P x 7 6 5 8 4 9 6 6 5 7 4 8 5 6 4 7 - 3 P x - 2 P x + P x + 3 P x + P x + P x - 3 P x - P x 4 6 3 7 4 5 3 5 4 3 3 3 2 4 2 3 + P x + P x + 3 P x - P x + 3 P x - 3 P x + P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 1}, {3 r + 3} 20 30 19 30 19 29 19 27 18 27 17 27 17 26 P x - P x + P x - P x + P x - 4 P x + 2 P x 16 27 16 26 17 24 16 25 16 24 16 23 + 7 P x - 3 P x - 3 P x + 3 P x + 10 P x - 3 P x 15 24 15 23 14 24 16 21 14 23 13 24 - 5 P x - P x + 5 P x + 3 P x - P x - 5 P x 15 21 14 22 13 23 14 21 13 22 14 20 - 3 P x + 6 P x + 10 P x + 12 P x - 5 P x - 4 P x 13 21 13 20 12 21 14 18 13 19 12 20 - 21 P x + 13 P x + 10 P x + 3 P x - 3 P x - 2 P x 11 21 13 18 12 19 11 20 10 21 13 17 - 2 P x - 14 P x - P x + 4 P x + P x + 6 P x 12 18 11 19 10 20 12 17 11 18 10 19 + 13 P x - 2 P x - 4 P x - P x - 15 P x + 6 P x 13 15 11 17 10 18 12 15 11 16 10 17 - 3 P x + 7 P x + 13 P x + 3 P x - P x - 15 P x 9 18 11 15 10 16 9 17 11 14 10 15 - 2 P x - 10 P x + 4 P x + 4 P x + 2 P x + 16 P x 9 16 10 14 9 15 11 12 10 13 9 14 - 2 P x - 12 P x - 15 P x - P x + 6 P x + 7 P x 8 15 10 12 9 13 8 14 7 15 10 11 + 10 P x + 10 P x - P x - 2 P x - 5 P x - 4 P x 9 12 8 13 7 14 9 11 8 12 7 13 - 10 P x - P x + 10 P x + 2 P x + 13 P x - 5 P x 10 9 8 11 7 12 9 9 7 11 6 12 8 9 + P x - P x - 21 P x - P x + 13 P x + 5 P x + 3 P x 7 10 6 11 7 9 6 10 7 8 6 9 6 8 - 3 P x - P x - 14 P x + 6 P x + 6 P x + 12 P x - 4 P x 5 9 7 6 5 8 4 9 6 6 4 8 5 6 - 5 P x - 3 P x - P x + 7 P x + 3 P x - 3 P x - 3 P x 4 7 4 6 4 5 3 6 3 5 4 3 3 3 + 3 P x + 10 P x - 3 P x - 4 P x + 2 P x + 3 P x - 3 P x 2 3 3 2 + P x - P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 1}, {3 r + 1, 3 r + 2} 20 30 19 27 18 27 16 27 17 24 14 24 16 21 P x - P x + P x + P x - 3 P x + 2 P x + 3 P x 15 21 14 21 12 21 14 18 13 18 12 18 - 3 P x + 3 P x - P x + 3 P x - 3 P x + 3 P x 13 15 10 18 12 15 11 15 11 12 8 15 - 3 P x - 4 P x + 3 P x - 6 P x - P x - P x 10 12 9 12 8 12 10 9 9 9 6 12 8 9 + 6 P x - 6 P x + 3 P x + P x - P x + 2 P x + 3 P x 7 9 6 9 7 6 4 9 6 6 5 6 4 3 - 3 P x + 3 P x - 3 P x + P x + 3 P x - 3 P x + 3 P x 3 3 2 3 - 3 P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 1}, {3 r + 1, 3 r + 3} 20 30 19 30 19 29 19 27 18 27 17 27 17 26 P x - P x + P x - P x + P x - 3 P x + 3 P x 16 27 16 26 17 24 16 25 16 24 16 23 + 4 P x - 6 P x - 3 P x + 3 P x + 6 P x - 6 P x 15 24 15 23 14 24 16 21 14 23 13 24 - 3 P x + 3 P x + 5 P x + 3 P x - 6 P x - 3 P x 15 21 14 22 13 23 14 21 13 22 14 20 - 3 P x + 3 P x + 9 P x + 9 P x - 9 P x - 6 P x 13 21 13 20 12 21 14 18 13 19 12 20 - 9 P x + 21 P x + 2 P x + 3 P x - 9 P x - 6 P x 11 21 13 18 12 19 11 20 10 21 13 17 - P x - 12 P x + 3 P x + 3 P x + P x + 9 P x 12 18 11 19 10 20 12 17 11 18 10 19 + 9 P x - 3 P x - 4 P x - 6 P x - 8 P x + 6 P x 13 15 11 17 10 18 12 15 11 16 10 17 - 3 P x + 12 P x + 2 P x + 3 P x - 3 P x - 23 P x 9 18 11 15 10 16 9 17 11 14 10 15 - P x - 9 P x + 18 P x + 3 P x + 3 P x + 14 P x 9 16 10 14 9 15 11 12 10 13 9 14 - 3 P x - 24 P x - 8 P x - P x + 6 P x + 12 P x 8 15 10 12 9 13 8 14 7 15 10 11 + 2 P x + 10 P x - 3 P x - 6 P x - 3 P x - 4 P x 9 12 8 13 7 14 9 11 8 12 7 13 10 9 - 9 P x + 3 P x + 9 P x + 3 P x + 9 P x - 9 P x + P x 8 11 7 12 9 9 7 11 6 12 8 9 7 10 - 6 P x - 9 P x - P x + 21 P x + 5 P x + 3 P x - 9 P x 6 11 7 9 6 10 7 8 6 9 6 8 5 9 - 6 P x - 12 P x + 3 P x + 9 P x + 9 P x - 6 P x - 3 P x 7 6 5 8 4 9 6 6 4 8 5 6 4 7 - 3 P x + 3 P x + 4 P x + 3 P x - 6 P x - 3 P x + 3 P x 4 6 4 5 3 6 3 5 4 3 3 3 2 3 3 + 6 P x - 6 P x - 3 P x + 3 P x + 3 P x - 3 P x + P x - P x 2 + P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 1}, {3 r + 2, 3 r + 3} 20 30 19 30 19 27 18 27 17 27 17 26 16 27 P x - P x - P x + P x - 3 P x - P x + 3 P x 16 26 17 24 16 24 16 23 15 24 15 23 + 3 P x - 3 P x + 7 P x + 3 P x - P x - 4 P x 14 24 16 21 14 23 13 24 15 21 14 22 + 2 P x + 3 P x + 2 P x - 2 P x - 3 P x - P x 13 23 14 21 14 20 13 21 13 20 12 21 - 3 P x + 10 P x + 2 P x - 9 P x - 12 P x + 3 P x 14 18 12 20 11 21 13 18 12 19 11 20 + 3 P x + 4 P x - P x - 11 P x + 4 P x - P x 10 21 13 17 12 18 12 17 11 18 13 15 + P x - 3 P x + 8 P x + 5 P x - 8 P x - 3 P x 11 17 10 18 12 15 10 17 9 18 11 15 - 7 P x + 5 P x + 3 P x + 6 P x - P x - 9 P x 10 16 9 17 11 14 10 15 10 14 9 15 + 10 P x - P x - P x + 8 P x + 12 P x - 8 P x 11 12 9 14 8 15 10 12 8 14 7 15 - P x - 7 P x + 3 P x + 10 P x + 4 P x - 2 P x 9 12 8 13 7 14 9 11 8 12 10 9 8 11 - 9 P x + 4 P x - 3 P x - P x + 8 P x + P x + 5 P x 7 12 9 9 7 11 6 12 8 9 6 11 7 9 - 9 P x - P x - 12 P x + 2 P x + 3 P x + 2 P x - 11 P x 6 10 7 8 6 9 6 8 5 9 7 6 5 8 - P x - 3 P x + 10 P x + 2 P x - P x - 3 P x - 4 P x 4 9 6 6 4 8 5 6 4 6 4 5 3 6 + 3 P x + 3 P x + 3 P x - 3 P x + 7 P x + 3 P x - 3 P x 3 5 4 3 3 3 2 3 3 - P x + 3 P x - 3 P x + P x - P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 1}, {3 r + 1, 3 r + 2, 3 r + 3} P - 1 = 0 ---------------------------- (A,B)= , {3 r + 2}, {} 4 3 P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 2}, {3 r + 1} 20 30 19 27 18 28 18 27 17 28 17 26 16 27 16 26 P x - P x + P x + P x + P x - P x + P x + P x 17 24 16 25 16 24 15 25 16 23 15 24 - 3 P x - P x + P x + 3 P x + 3 P x + 3 P x 15 23 14 24 16 21 15 22 14 23 15 21 - 2 P x + 2 P x + 3 P x + P x + 5 P x - 3 P x 14 22 14 21 13 22 14 20 13 21 13 20 - 7 P x + 4 P x - P x + 2 P x + 6 P x - 7 P x 12 21 14 18 13 19 12 20 13 18 12 19 - 3 P x + 3 P x + 5 P x + 4 P x - 2 P x - 3 P x 11 20 13 17 12 18 11 19 12 17 11 18 + P x - 3 P x + 2 P x - 11 P x + 6 P x + 11 P x 10 19 13 15 12 16 11 17 10 18 12 15 + P x - 3 P x - 2 P x - 10 P x - 7 P x + 3 P x 11 16 10 17 11 15 10 16 9 17 11 14 + 10 P x - 4 P x - 6 P x + 4 P x + P x - P x 10 15 9 16 10 14 9 15 11 12 10 13 - 10 P x - 11 P x + 12 P x + 11 P x - P x - 4 P x 9 14 8 15 10 12 9 13 8 14 9 12 - 10 P x - 3 P x + 6 P x + 10 P x + 4 P x - 6 P x 8 13 9 11 8 12 7 13 10 9 8 11 7 12 - 3 P x - P x + 2 P x - P x + P x + 6 P x + 6 P x 9 9 8 10 7 11 6 12 8 9 7 10 6 11 - P x - 2 P x - 7 P x + 2 P x + 3 P x + 5 P x + 5 P x 7 9 6 10 7 8 6 9 5 10 6 8 5 9 - 2 P x - 7 P x - 3 P x + 4 P x + 3 P x + 2 P x + 3 P x 7 6 5 8 4 9 6 6 5 7 4 8 5 6 4 7 - 3 P x - 2 P x + P x + 3 P x + P x + P x - 3 P x - P x 4 6 3 7 4 5 3 5 4 3 3 3 2 4 2 3 + P x + P x + 3 P x - P x + 3 P x - 3 P x + P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 2}, {3 r + 2} 8 12 7 11 7 10 7 9 6 10 6 9 6 8 5 9 P x - 2 P x + P x - P x + 2 P x - P x + 2 P x - 2 P x 5 8 4 8 5 6 4 7 4 5 3 6 4 4 3 5 - P x + P x - P x + 4 P x + P x - 2 P x - 2 P x - P x 4 3 3 3 2 4 2 3 2 2 2 + P x - P x + 2 P x - P x + 2 P x - 2 P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 2}, {3 r + 3} 20 30 19 30 19 28 19 27 18 28 18 27 17 27 17 26 P x - P x + P x - P x + P x + P x - 4 P x + P x 16 27 17 25 17 24 16 25 16 24 15 25 + 7 P x + 3 P x - 3 P x - 9 P x + 10 P x + 4 P x 16 23 15 24 16 22 14 24 16 21 15 22 + 3 P x - 5 P x - 6 P x + 5 P x + 3 P x + 6 P x 14 23 13 24 15 21 14 22 14 21 13 22 + 3 P x - 5 P x - 3 P x - 11 P x + 10 P x + 20 P x 14 20 13 21 12 22 14 19 13 20 12 21 + 5 P x - 21 P x - P x - 6 P x - 14 P x + 10 P x 14 18 13 19 12 20 11 21 13 18 12 19 + 3 P x + 29 P x + 4 P x - 2 P x - 11 P x - 19 P x 10 21 13 17 12 18 11 19 13 16 12 17 + P x - 9 P x + 12 P x + 15 P x + 9 P x + 5 P x 11 18 10 19 13 15 12 16 11 17 10 18 - 15 P x - 8 P x - 3 P x - 7 P x - 14 P x + 17 P x 12 15 11 16 10 17 9 18 11 15 10 16 + 3 P x + 19 P x + 13 P x - 2 P x - 9 P x - 44 P x 11 14 10 15 9 16 11 13 10 14 9 15 - 3 P x + 16 P x + 15 P x + 3 P x + 22 P x - 15 P x 8 16 11 12 10 13 9 14 8 15 10 12 - P x - P x - 27 P x - 14 P x + 10 P x + 6 P x 9 13 8 14 7 15 10 11 9 12 8 13 + 19 P x + 4 P x - 5 P x + 6 P x - 9 P x - 19 P x 10 10 9 11 8 12 7 13 10 9 9 10 - 4 P x - 3 P x + 12 P x + 20 P x + P x + 3 P x 8 11 7 12 9 9 8 10 7 11 6 12 8 9 + 5 P x - 21 P x - P x - 7 P x - 14 P x + 5 P x + 3 P x 7 10 6 11 7 9 6 10 7 8 6 9 + 29 P x + 3 P x - 11 P x - 11 P x - 9 P x + 10 P x 5 10 7 7 6 8 5 9 7 6 6 7 4 9 + 4 P x + 9 P x + 5 P x - 5 P x - 3 P x - 6 P x + 7 P x 6 6 5 7 5 6 4 7 4 6 4 5 3 6 + 3 P x + 6 P x - 3 P x - 9 P x + 10 P x + 3 P x - 4 P x 4 4 3 5 4 3 3 4 3 3 2 4 2 3 3 - 6 P x + P x + 3 P x + 3 P x - 3 P x + P x + P x - P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 2}, {3 r + 1, 3 r + 2} 20 30 19 27 18 27 17 24 15 24 16 21 15 21 P x - P x + P x - 3 P x + 2 P x + 3 P x - 3 P x 14 21 13 21 14 18 13 18 12 18 11 18 + 2 P x + P x + 3 P x - 2 P x + 3 P x + P x 13 15 10 18 12 15 11 15 10 15 9 15 - 3 P x + P x + 3 P x - 6 P x - 6 P x + P x 11 12 10 12 9 12 8 12 10 9 7 12 9 9 - P x + 6 P x - 6 P x + 3 P x + P x + P x - P x 8 9 7 9 6 9 5 9 7 6 6 6 5 6 + 3 P x - 2 P x + 2 P x + 2 P x - 3 P x + 3 P x - 3 P x 4 3 3 3 2 3 + 3 P x - 3 P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 2}, {3 r + 1, 3 r + 3} 20 30 19 30 19 27 18 28 18 27 17 27 16 27 P x - P x - P x + P x + P x - 3 P x + 4 P x 17 24 16 25 16 24 15 25 15 24 14 24 - 3 P x - P x + 7 P x + P x - 3 P x + 5 P x 16 21 15 22 14 23 13 24 15 21 14 22 + 3 P x + P x + P x - 3 P x - 3 P x - 8 P x 14 21 13 22 13 21 12 22 12 21 14 18 + 11 P x + 5 P x - 12 P x - 2 P x + 2 P x + 3 P x 13 19 12 20 11 21 13 18 12 19 10 21 + 5 P x + 4 P x - P x - 12 P x - 11 P x + P x 12 18 11 19 11 18 10 19 13 15 12 16 + 8 P x + 10 P x - 9 P x - 4 P x - 3 P x - 2 P x 10 18 12 15 11 16 10 17 9 18 11 15 + 6 P x + 3 P x + 10 P x + 6 P x - P x - 9 P x 10 16 10 15 9 16 9 15 8 16 11 12 - 10 P x + 14 P x + 10 P x - 9 P x - 2 P x - P x 10 13 8 15 10 12 9 13 8 14 7 15 - 4 P x + 2 P x + 10 P x + 10 P x + 4 P x - 3 P x 9 12 8 13 8 12 7 13 10 9 7 12 9 9 - 9 P x - 11 P x + 8 P x + 5 P x + P x - 12 P x - P x 8 10 6 12 8 9 7 10 6 11 7 9 6 10 - 2 P x + 5 P x + 3 P x + 5 P x + P x - 12 P x - 8 P x 6 9 5 10 5 9 7 6 4 9 6 6 5 7 + 11 P x + P x - 3 P x - 3 P x + 4 P x + 3 P x + P x 5 6 4 7 4 6 3 6 4 3 3 3 2 4 2 3 - 3 P x - P x + 7 P x - 3 P x + 3 P x - 3 P x + P x + P x 3 - P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 2}, {3 r + 2, 3 r + 3} 20 30 19 30 19 28 19 27 18 27 17 27 16 27 P x - P x + P x - P x + P x - 3 P x + 3 P x 17 25 17 24 16 25 16 24 16 23 15 24 + 3 P x - 3 P x - 6 P x + 6 P x + 3 P x - P x 16 22 14 24 16 21 15 22 13 24 15 21 - 6 P x + 2 P x + 3 P x + 3 P x - 2 P x - 3 P x 14 22 14 21 13 22 14 20 13 21 14 19 - 5 P x + 8 P x + 7 P x + 3 P x - 9 P x - 6 P x 13 20 12 21 14 18 13 19 11 21 13 18 - 8 P x + 3 P x + 3 P x + 19 P x - P x - 8 P x 12 19 10 21 13 17 12 18 11 19 13 16 - 6 P x + P x - 9 P x + 9 P x + 3 P x + 9 P x 12 17 11 18 10 19 13 15 12 16 11 17 + 3 P x - 8 P x - 4 P x - 3 P x - 6 P x - 3 P x 10 18 12 15 11 16 10 17 9 18 11 15 + 5 P x + 3 P x + 12 P x + 6 P x - P x - 8 P x 10 16 11 14 10 15 9 16 11 13 10 14 - 18 P x - 3 P x + 8 P x + 3 P x + 3 P x + 18 P x 9 15 11 12 10 13 9 14 8 15 10 12 - 8 P x - P x - 23 P x - 3 P x + 3 P x + 6 P x 9 13 7 15 10 11 9 12 8 13 10 10 + 12 P x - 2 P x + 6 P x - 8 P x - 6 P x - 4 P x 9 11 8 12 7 13 10 9 9 10 8 11 7 12 - 3 P x + 9 P x + 7 P x + P x + 3 P x + 3 P x - 9 P x 9 9 8 10 7 11 6 12 8 9 7 10 7 9 - P x - 6 P x - 8 P x + 2 P x + 3 P x + 19 P x - 8 P x 6 10 7 8 6 9 7 7 6 8 5 9 7 6 - 5 P x - 9 P x + 8 P x + 9 P x + 3 P x - P x - 3 P x 6 7 4 9 6 6 5 7 5 6 4 7 4 6 - 6 P x + 3 P x + 3 P x + 3 P x - 3 P x - 6 P x + 6 P x 4 5 3 6 4 4 4 3 3 4 3 3 2 3 3 + 3 P x - 3 P x - 6 P x + 3 P x + 3 P x - 3 P x + P x - P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 2}, {3 r + 1, 3 r + 2, 3 r + 3} P - 1 = 0 ---------------------------- (A,B)= , {3 r + 3}, {} 4 3 3 3 2 2 P x - P x + P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 3}, {3 r + 1} 20 30 19 30 19 29 19 27 18 27 17 27 17 26 P x - P x + P x - P x + P x - 4 P x + 2 P x 16 27 16 26 17 24 16 25 16 24 16 23 + 7 P x - 3 P x - 3 P x + 3 P x + 10 P x - 3 P x 15 24 15 23 14 24 16 21 14 23 13 24 - 5 P x - P x + 5 P x + 3 P x - P x - 5 P x 15 21 14 22 13 23 14 21 13 22 14 20 - 3 P x + 6 P x + 10 P x + 12 P x - 5 P x - 4 P x 13 21 13 20 12 21 14 18 13 19 12 20 - 21 P x + 13 P x + 10 P x + 3 P x - 3 P x - 2 P x 11 21 13 18 12 19 11 20 10 21 13 17 - 2 P x - 14 P x - P x + 4 P x + P x + 6 P x 12 18 11 19 10 20 12 17 11 18 10 19 + 13 P x - 2 P x - 4 P x - P x - 15 P x + 6 P x 13 15 11 17 10 18 12 15 11 16 10 17 - 3 P x + 7 P x + 13 P x + 3 P x - P x - 15 P x 9 18 11 15 10 16 9 17 11 14 10 15 - 2 P x - 10 P x + 4 P x + 4 P x + 2 P x + 16 P x 9 16 10 14 9 15 11 12 10 13 9 14 - 2 P x - 12 P x - 15 P x - P x + 6 P x + 7 P x 8 15 10 12 9 13 8 14 7 15 10 11 + 10 P x + 10 P x - P x - 2 P x - 5 P x - 4 P x 9 12 8 13 7 14 9 11 8 12 7 13 - 10 P x - P x + 10 P x + 2 P x + 13 P x - 5 P x 10 9 8 11 7 12 9 9 7 11 6 12 8 9 + P x - P x - 21 P x - P x + 13 P x + 5 P x + 3 P x 7 10 6 11 7 9 6 10 7 8 6 9 6 8 - 3 P x - P x - 14 P x + 6 P x + 6 P x + 12 P x - 4 P x 5 9 7 6 5 8 4 9 6 6 4 8 5 6 - 5 P x - 3 P x - P x + 7 P x + 3 P x - 3 P x - 3 P x 4 7 4 6 4 5 3 6 3 5 4 3 3 3 + 3 P x + 10 P x - 3 P x - 4 P x + 2 P x + 3 P x - 3 P x 2 3 3 2 + P x - P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 3}, {3 r + 2} 20 30 19 30 19 28 19 27 18 28 18 27 17 27 17 26 P x - P x + P x - P x + P x + P x - 4 P x + P x 16 27 17 25 17 24 16 25 16 24 15 25 + 7 P x + 3 P x - 3 P x - 9 P x + 10 P x + 4 P x 16 23 15 24 16 22 14 24 16 21 15 22 + 3 P x - 5 P x - 6 P x + 5 P x + 3 P x + 6 P x 14 23 13 24 15 21 14 22 14 21 13 22 + 3 P x - 5 P x - 3 P x - 11 P x + 10 P x + 20 P x 14 20 13 21 12 22 14 19 13 20 12 21 + 5 P x - 21 P x - P x - 6 P x - 14 P x + 10 P x 14 18 13 19 12 20 11 21 13 18 12 19 + 3 P x + 29 P x + 4 P x - 2 P x - 11 P x - 19 P x 10 21 13 17 12 18 11 19 13 16 12 17 + P x - 9 P x + 12 P x + 15 P x + 9 P x + 5 P x 11 18 10 19 13 15 12 16 11 17 10 18 - 15 P x - 8 P x - 3 P x - 7 P x - 14 P x + 17 P x 12 15 11 16 10 17 9 18 11 15 10 16 + 3 P x + 19 P x + 13 P x - 2 P x - 9 P x - 44 P x 11 14 10 15 9 16 11 13 10 14 9 15 - 3 P x + 16 P x + 15 P x + 3 P x + 22 P x - 15 P x 8 16 11 12 10 13 9 14 8 15 10 12 - P x - P x - 27 P x - 14 P x + 10 P x + 6 P x 9 13 8 14 7 15 10 11 9 12 8 13 + 19 P x + 4 P x - 5 P x + 6 P x - 9 P x - 19 P x 10 10 9 11 8 12 7 13 10 9 9 10 - 4 P x - 3 P x + 12 P x + 20 P x + P x + 3 P x 8 11 7 12 9 9 8 10 7 11 6 12 8 9 + 5 P x - 21 P x - P x - 7 P x - 14 P x + 5 P x + 3 P x 7 10 6 11 7 9 6 10 7 8 6 9 + 29 P x + 3 P x - 11 P x - 11 P x - 9 P x + 10 P x 5 10 7 7 6 8 5 9 7 6 6 7 4 9 + 4 P x + 9 P x + 5 P x - 5 P x - 3 P x - 6 P x + 7 P x 6 6 5 7 5 6 4 7 4 6 4 5 3 6 + 3 P x + 6 P x - 3 P x - 9 P x + 10 P x + 3 P x - 4 P x 4 4 3 5 4 3 3 4 3 3 2 4 2 3 3 - 6 P x + P x + 3 P x + 3 P x - 3 P x + P x + P x - P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 3}, {3 r + 3} 8 12 7 12 7 11 7 10 7 9 5 9 5 8 4 9 5 7 P x - P x + P x + P x - P x + P x - P x + P x - P x 4 8 5 6 4 7 4 6 4 5 3 6 4 4 3 5 - 2 P x + P x - P x + 2 P x - P x + P x - 2 P x - P x 4 3 3 4 3 3 3 2 + P x - P x + P x - P x + P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 3}, {3 r + 1, 3 r + 2} 20 30 19 30 19 27 18 27 17 27 16 27 17 24 P x - P x - P x + P x - 4 P x + 7 P x - 3 P x 16 24 15 24 14 24 16 21 13 24 15 21 + 9 P x - 5 P x + 5 P x + 3 P x - 5 P x - 3 P x 14 21 13 21 12 21 14 18 11 21 + 10 P x - 21 P x + 10 P x + 3 P x - 2 P x 13 18 10 21 12 18 11 18 13 15 10 18 - 14 P x + P x + 14 P x - 15 P x - 3 P x + 17 P x 12 15 9 18 11 15 10 15 9 15 11 12 + 3 P x - 2 P x - 10 P x + 24 P x - 15 P x - P x 8 15 10 12 7 15 9 12 8 12 10 9 + 10 P x + 10 P x - 5 P x - 10 P x + 14 P x + P x 7 12 9 9 6 12 8 9 7 9 6 9 5 9 - 21 P x - P x + 5 P x + 3 P x - 14 P x + 10 P x - 5 P x 7 6 4 9 6 6 5 6 4 6 3 6 4 3 - 3 P x + 7 P x + 3 P x - 3 P x + 9 P x - 4 P x + 3 P x 3 3 2 3 3 - 3 P x + P x - P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 3}, {3 r + 1, 3 r + 3} 20 30 19 30 19 29 19 27 18 27 17 27 17 26 P x - P x + P x - P x + P x - 3 P x + 3 P x 16 27 16 26 17 24 16 25 16 24 16 23 + 3 P x - 6 P x - 3 P x + 3 P x + 7 P x - 6 P x 15 24 15 23 14 24 16 21 14 23 13 24 - 3 P x + 3 P x + 3 P x + 3 P x - 6 P x - 3 P x 15 21 14 22 13 23 14 21 13 22 14 20 - 3 P x + 3 P x + 9 P x + 11 P x - 9 P x - 6 P x 13 21 13 20 12 21 14 18 13 19 12 20 - 9 P x + 21 P x + 3 P x + 3 P x - 9 P x - 6 P x 11 21 13 18 12 19 11 20 10 21 13 17 - P x - 12 P x + 3 P x + 3 P x + P x + 9 P x 12 18 11 19 10 20 12 17 11 18 10 19 + 8 P x - 3 P x - 4 P x - 6 P x - 8 P x + 6 P x 13 15 11 17 10 18 12 15 11 16 10 17 - 3 P x + 12 P x + 6 P x + 3 P x - 3 P x - 23 P x 9 18 11 15 10 16 9 17 11 14 10 15 - P x - 9 P x + 18 P x + 3 P x + 3 P x + 10 P x 9 16 10 14 9 15 11 12 10 13 9 14 - 3 P x - 24 P x - 8 P x - P x + 6 P x + 12 P x 8 15 10 12 9 13 8 14 7 15 10 11 + 3 P x + 10 P x - 3 P x - 6 P x - 3 P x - 4 P x 9 12 8 13 7 14 9 11 8 12 7 13 10 9 - 9 P x + 3 P x + 9 P x + 3 P x + 8 P x - 9 P x + P x 8 11 7 12 9 9 7 11 6 12 8 9 7 10 - 6 P x - 9 P x - P x + 21 P x + 3 P x + 3 P x - 9 P x 6 11 7 9 6 10 7 8 6 9 6 8 5 9 - 6 P x - 12 P x + 3 P x + 9 P x + 11 P x - 6 P x - 3 P x 7 6 5 8 4 9 6 6 4 8 5 6 4 7 - 3 P x + 3 P x + 3 P x + 3 P x - 6 P x - 3 P x + 3 P x 4 6 4 5 3 6 3 5 4 3 3 3 2 3 3 + 7 P x - 6 P x - 3 P x + 3 P x + 3 P x - 3 P x + P x - P x 2 + P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 3}, {3 r + 2, 3 r + 3} 20 30 19 30 19 28 19 27 18 27 17 27 16 27 P x - P x + P x - P x + P x - 3 P x + 3 P x 17 25 17 24 16 25 16 24 16 23 15 24 + 3 P x - 3 P x - 6 P x + 7 P x + 3 P x - 3 P x 16 22 14 24 16 21 15 22 13 24 15 21 - 6 P x + 3 P x + 3 P x + 3 P x - 3 P x - 3 P x 14 22 14 21 13 22 14 20 13 21 14 19 - 6 P x + 11 P x + 9 P x + 3 P x - 12 P x - 6 P x 13 20 12 21 14 18 13 19 11 21 13 18 - 9 P x + 3 P x + 3 P x + 21 P x - P x - 9 P x 12 19 10 21 13 17 12 18 11 19 13 16 - 6 P x + P x - 9 P x + 8 P x + 3 P x + 9 P x 12 17 11 18 10 19 13 15 12 16 11 17 + 3 P x - 9 P x - 4 P x - 3 P x - 6 P x - 3 P x 10 18 12 15 11 16 10 17 9 18 11 15 + 10 P x + 3 P x + 12 P x + 6 P x - P x - 8 P x 10 16 11 14 10 15 9 16 11 13 10 14 - 24 P x - 3 P x + 10 P x + 3 P x + 3 P x + 18 P x 9 15 11 12 10 13 9 14 8 15 10 12 - 9 P x - P x - 23 P x - 3 P x + 3 P x + 6 P x 9 13 7 15 10 11 9 12 8 13 10 10 + 12 P x - 3 P x + 6 P x - 8 P x - 6 P x - 4 P x 9 11 8 12 7 13 10 9 9 10 8 11 - 3 P x + 8 P x + 9 P x + P x + 3 P x + 3 P x 7 12 9 9 8 10 7 11 6 12 8 9 7 10 - 12 P x - P x - 6 P x - 9 P x + 3 P x + 3 P x + 21 P x 7 9 6 10 7 8 6 9 7 7 6 8 5 9 - 9 P x - 6 P x - 9 P x + 11 P x + 9 P x + 3 P x - 3 P x 7 6 6 7 4 9 6 6 5 7 5 6 4 7 - 3 P x - 6 P x + 3 P x + 3 P x + 3 P x - 3 P x - 6 P x 4 6 4 5 3 6 4 4 4 3 3 4 3 3 + 7 P x + 3 P x - 3 P x - 6 P x + 3 P x + 3 P x - 3 P x 2 3 3 + P x - P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 3}, {3 r + 1, 3 r + 2, 3 r + 3} P - 1 = 0 ---------------------------- (A,B)= , {3 r + 1, 3 r + 2}, {} 4 3 P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 1, 3 r + 2}, {3 r + 1} 20 30 19 27 18 27 16 27 17 24 14 24 16 21 P x - P x + P x + P x - 3 P x + 2 P x + 3 P x 15 21 14 21 12 21 14 18 13 18 12 18 - 3 P x + 3 P x - P x + 3 P x - 3 P x + 3 P x 13 15 10 18 12 15 11 15 11 12 8 15 - 3 P x - 4 P x + 3 P x - 6 P x - P x - P x 10 12 9 12 8 12 10 9 9 9 6 12 8 9 + 6 P x - 6 P x + 3 P x + P x - P x + 2 P x + 3 P x 7 9 6 9 7 6 4 9 6 6 5 6 4 3 - 3 P x + 3 P x - 3 P x + P x + 3 P x - 3 P x + 3 P x 3 3 2 3 - 3 P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 1, 3 r + 2}, {3 r + 2} 20 30 19 27 18 27 17 24 15 24 16 21 15 21 P x - P x + P x - 3 P x + 2 P x + 3 P x - 3 P x 14 21 13 21 14 18 13 18 12 18 11 18 + 2 P x + P x + 3 P x - 2 P x + 3 P x + P x 13 15 10 18 12 15 11 15 10 15 9 15 - 3 P x + P x + 3 P x - 6 P x - 6 P x + P x 11 12 10 12 9 12 8 12 10 9 7 12 9 9 - P x + 6 P x - 6 P x + 3 P x + P x + P x - P x 8 9 7 9 6 9 5 9 7 6 6 6 5 6 + 3 P x - 2 P x + 2 P x + 2 P x - 3 P x + 3 P x - 3 P x 4 3 3 3 2 3 + 3 P x - 3 P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 1, 3 r + 2}, {3 r + 3} 20 30 19 30 19 27 18 27 17 27 16 27 17 24 P x - P x - P x + P x - 4 P x + 7 P x - 3 P x 16 24 15 24 14 24 16 21 13 24 15 21 + 9 P x - 5 P x + 5 P x + 3 P x - 5 P x - 3 P x 14 21 13 21 12 21 14 18 11 21 + 10 P x - 21 P x + 10 P x + 3 P x - 2 P x 13 18 10 21 12 18 11 18 13 15 10 18 - 14 P x + P x + 14 P x - 15 P x - 3 P x + 17 P x 12 15 9 18 11 15 10 15 9 15 11 12 + 3 P x - 2 P x - 10 P x + 24 P x - 15 P x - P x 8 15 10 12 7 15 9 12 8 12 10 9 + 10 P x + 10 P x - 5 P x - 10 P x + 14 P x + P x 7 12 9 9 6 12 8 9 7 9 6 9 5 9 - 21 P x - P x + 5 P x + 3 P x - 14 P x + 10 P x - 5 P x 7 6 4 9 6 6 5 6 4 6 3 6 4 3 - 3 P x + 7 P x + 3 P x - 3 P x + 9 P x - 4 P x + 3 P x 3 3 2 3 3 - 3 P x + P x - P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 1, 3 r + 2}, {3 r + 1, 3 r + 2} 2 3 P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 1, 3 r + 2}, {3 r + 1, 3 r + 3} 20 30 19 30 19 27 18 27 17 27 16 27 17 24 P x - P x - P x + P x - 3 P x + 4 P x - 3 P x 16 24 15 24 14 24 16 21 13 24 15 21 + 6 P x - 3 P x + 5 P x + 3 P x - 3 P x - 3 P x 14 21 13 21 12 21 14 18 11 21 13 18 + 9 P x - 12 P x + 2 P x + 3 P x - P x - 12 P x 10 21 12 18 11 18 13 15 10 18 12 15 + P x + 9 P x - 9 P x - 3 P x + 6 P x + 3 P x 9 18 11 15 10 15 9 15 11 12 8 15 - P x - 9 P x + 18 P x - 9 P x - P x + 2 P x 10 12 7 15 9 12 8 12 10 9 7 12 9 9 + 10 P x - 3 P x - 9 P x + 9 P x + P x - 12 P x - P x 6 12 8 9 7 9 6 9 5 9 7 6 4 9 + 5 P x + 3 P x - 12 P x + 9 P x - 3 P x - 3 P x + 4 P x 6 6 5 6 4 6 3 6 4 3 3 3 2 3 3 + 3 P x - 3 P x + 6 P x - 3 P x + 3 P x - 3 P x + P x - P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 1, 3 r + 2}, {3 r + 2, 3 r + 3} 20 30 19 30 19 27 18 27 17 27 16 27 17 24 P x - P x - P x + P x - 3 P x + 3 P x - 3 P x 16 24 15 24 14 24 16 21 13 24 15 21 + 6 P x - P x + 2 P x + 3 P x - 2 P x - 3 P x 14 21 13 21 12 21 14 18 11 21 13 18 + 8 P x - 9 P x + 3 P x + 3 P x - P x - 11 P x 10 21 12 18 11 18 13 15 10 18 12 15 + P x + 9 P x - 8 P x - 3 P x + 5 P x + 3 P x 9 18 11 15 10 15 9 15 11 12 8 15 - P x - 9 P x + 12 P x - 8 P x - P x + 3 P x 10 12 7 15 9 12 8 12 10 9 7 12 9 9 + 10 P x - 2 P x - 9 P x + 9 P x + P x - 9 P x - P x 6 12 8 9 7 9 6 9 5 9 7 6 4 9 + 2 P x + 3 P x - 11 P x + 8 P x - P x - 3 P x + 3 P x 6 6 5 6 4 6 3 6 4 3 3 3 2 3 3 + 3 P x - 3 P x + 6 P x - 3 P x + 3 P x - 3 P x + P x - P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 1, 3 r + 2}, {3 r + 1, 3 r + 2, 3 r + 3} P - 1 = 0 ---------------------------- (A,B)= , {3 r + 1, 3 r + 3}, {} 4 3 3 3 2 2 P x - P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 1, 3 r + 3}, {3 r + 1} 20 30 19 30 19 29 19 27 18 27 17 27 17 26 P x - P x + P x - P x + P x - 3 P x + 3 P x 16 27 16 26 17 24 16 25 16 24 16 23 + 4 P x - 6 P x - 3 P x + 3 P x + 6 P x - 6 P x 15 24 15 23 14 24 16 21 14 23 13 24 - 3 P x + 3 P x + 5 P x + 3 P x - 6 P x - 3 P x 15 21 14 22 13 23 14 21 13 22 14 20 - 3 P x + 3 P x + 9 P x + 9 P x - 9 P x - 6 P x 13 21 13 20 12 21 14 18 13 19 12 20 - 9 P x + 21 P x + 2 P x + 3 P x - 9 P x - 6 P x 11 21 13 18 12 19 11 20 10 21 13 17 - P x - 12 P x + 3 P x + 3 P x + P x + 9 P x 12 18 11 19 10 20 12 17 11 18 10 19 + 9 P x - 3 P x - 4 P x - 6 P x - 8 P x + 6 P x 13 15 11 17 10 18 12 15 11 16 10 17 - 3 P x + 12 P x + 2 P x + 3 P x - 3 P x - 23 P x 9 18 11 15 10 16 9 17 11 14 10 15 - P x - 9 P x + 18 P x + 3 P x + 3 P x + 14 P x 9 16 10 14 9 15 11 12 10 13 9 14 - 3 P x - 24 P x - 8 P x - P x + 6 P x + 12 P x 8 15 10 12 9 13 8 14 7 15 10 11 + 2 P x + 10 P x - 3 P x - 6 P x - 3 P x - 4 P x 9 12 8 13 7 14 9 11 8 12 7 13 10 9 - 9 P x + 3 P x + 9 P x + 3 P x + 9 P x - 9 P x + P x 8 11 7 12 9 9 7 11 6 12 8 9 7 10 - 6 P x - 9 P x - P x + 21 P x + 5 P x + 3 P x - 9 P x 6 11 7 9 6 10 7 8 6 9 6 8 5 9 - 6 P x - 12 P x + 3 P x + 9 P x + 9 P x - 6 P x - 3 P x 7 6 5 8 4 9 6 6 4 8 5 6 4 7 - 3 P x + 3 P x + 4 P x + 3 P x - 6 P x - 3 P x + 3 P x 4 6 4 5 3 6 3 5 4 3 3 3 2 3 3 + 6 P x - 6 P x - 3 P x + 3 P x + 3 P x - 3 P x + P x - P x 2 + P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 1, 3 r + 3}, {3 r + 2} 20 30 19 30 19 27 18 28 18 27 17 27 16 27 P x - P x - P x + P x + P x - 3 P x + 4 P x 17 24 16 25 16 24 15 25 15 24 14 24 - 3 P x - P x + 7 P x + P x - 3 P x + 5 P x 16 21 15 22 14 23 13 24 15 21 14 22 + 3 P x + P x + P x - 3 P x - 3 P x - 8 P x 14 21 13 22 13 21 12 22 12 21 14 18 + 11 P x + 5 P x - 12 P x - 2 P x + 2 P x + 3 P x 13 19 12 20 11 21 13 18 12 19 10 21 + 5 P x + 4 P x - P x - 12 P x - 11 P x + P x 12 18 11 19 11 18 10 19 13 15 12 16 + 8 P x + 10 P x - 9 P x - 4 P x - 3 P x - 2 P x 10 18 12 15 11 16 10 17 9 18 11 15 + 6 P x + 3 P x + 10 P x + 6 P x - P x - 9 P x 10 16 10 15 9 16 9 15 8 16 11 12 - 10 P x + 14 P x + 10 P x - 9 P x - 2 P x - P x 10 13 8 15 10 12 9 13 8 14 7 15 - 4 P x + 2 P x + 10 P x + 10 P x + 4 P x - 3 P x 9 12 8 13 8 12 7 13 10 9 7 12 9 9 - 9 P x - 11 P x + 8 P x + 5 P x + P x - 12 P x - P x 8 10 6 12 8 9 7 10 6 11 7 9 6 10 - 2 P x + 5 P x + 3 P x + 5 P x + P x - 12 P x - 8 P x 6 9 5 10 5 9 7 6 4 9 6 6 5 7 + 11 P x + P x - 3 P x - 3 P x + 4 P x + 3 P x + P x 5 6 4 7 4 6 3 6 4 3 3 3 2 4 2 3 - 3 P x - P x + 7 P x - 3 P x + 3 P x - 3 P x + P x + P x 3 - P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 1, 3 r + 3}, {3 r + 3} 20 30 19 30 19 29 19 27 18 27 17 27 17 26 P x - P x + P x - P x + P x - 3 P x + 3 P x 16 27 16 26 17 24 16 25 16 24 16 23 + 3 P x - 6 P x - 3 P x + 3 P x + 7 P x - 6 P x 15 24 15 23 14 24 16 21 14 23 13 24 - 3 P x + 3 P x + 3 P x + 3 P x - 6 P x - 3 P x 15 21 14 22 13 23 14 21 13 22 14 20 - 3 P x + 3 P x + 9 P x + 11 P x - 9 P x - 6 P x 13 21 13 20 12 21 14 18 13 19 12 20 - 9 P x + 21 P x + 3 P x + 3 P x - 9 P x - 6 P x 11 21 13 18 12 19 11 20 10 21 13 17 - P x - 12 P x + 3 P x + 3 P x + P x + 9 P x 12 18 11 19 10 20 12 17 11 18 10 19 + 8 P x - 3 P x - 4 P x - 6 P x - 8 P x + 6 P x 13 15 11 17 10 18 12 15 11 16 10 17 - 3 P x + 12 P x + 6 P x + 3 P x - 3 P x - 23 P x 9 18 11 15 10 16 9 17 11 14 10 15 - P x - 9 P x + 18 P x + 3 P x + 3 P x + 10 P x 9 16 10 14 9 15 11 12 10 13 9 14 - 3 P x - 24 P x - 8 P x - P x + 6 P x + 12 P x 8 15 10 12 9 13 8 14 7 15 10 11 + 3 P x + 10 P x - 3 P x - 6 P x - 3 P x - 4 P x 9 12 8 13 7 14 9 11 8 12 7 13 10 9 - 9 P x + 3 P x + 9 P x + 3 P x + 8 P x - 9 P x + P x 8 11 7 12 9 9 7 11 6 12 8 9 7 10 - 6 P x - 9 P x - P x + 21 P x + 3 P x + 3 P x - 9 P x 6 11 7 9 6 10 7 8 6 9 6 8 5 9 - 6 P x - 12 P x + 3 P x + 9 P x + 11 P x - 6 P x - 3 P x 7 6 5 8 4 9 6 6 4 8 5 6 4 7 - 3 P x + 3 P x + 3 P x + 3 P x - 6 P x - 3 P x + 3 P x 4 6 4 5 3 6 3 5 4 3 3 3 2 3 3 + 7 P x - 6 P x - 3 P x + 3 P x + 3 P x - 3 P x + P x - P x 2 + P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 1, 3 r + 3}, {3 r + 1, 3 r + 2} 20 30 19 30 19 27 18 27 17 27 16 27 17 24 P x - P x - P x + P x - 3 P x + 4 P x - 3 P x 16 24 15 24 14 24 16 21 13 24 15 21 + 6 P x - 3 P x + 5 P x + 3 P x - 3 P x - 3 P x 14 21 13 21 12 21 14 18 11 21 13 18 + 9 P x - 12 P x + 2 P x + 3 P x - P x - 12 P x 10 21 12 18 11 18 13 15 10 18 12 15 + P x + 9 P x - 9 P x - 3 P x + 6 P x + 3 P x 9 18 11 15 10 15 9 15 11 12 8 15 - P x - 9 P x + 18 P x - 9 P x - P x + 2 P x 10 12 7 15 9 12 8 12 10 9 7 12 9 9 + 10 P x - 3 P x - 9 P x + 9 P x + P x - 12 P x - P x 6 12 8 9 7 9 6 9 5 9 7 6 4 9 + 5 P x + 3 P x - 12 P x + 9 P x - 3 P x - 3 P x + 4 P x 6 6 5 6 4 6 3 6 4 3 3 3 2 3 3 + 3 P x - 3 P x + 6 P x - 3 P x + 3 P x - 3 P x + P x - P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 1, 3 r + 3}, {3 r + 1, 3 r + 3} 2 3 3 2 P x - P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 1, 3 r + 3}, {3 r + 2, 3 r + 3} 20 30 19 30 19 27 18 27 17 27 16 27 17 24 P x - P x - P x + P x - 3 P x + 3 P x - 3 P x 16 24 15 24 14 24 16 21 13 24 15 21 + 7 P x - 3 P x + 3 P x + 3 P x - 3 P x - 3 P x 14 21 13 21 12 21 14 18 11 21 13 18 + 11 P x - 12 P x + 3 P x + 3 P x - P x - 12 P x 10 21 12 18 11 18 13 15 10 18 12 15 + P x + 8 P x - 9 P x - 3 P x + 10 P x + 3 P x 9 18 11 15 10 15 9 15 11 12 8 15 - P x - 9 P x + 14 P x - 9 P x - P x + 3 P x 10 12 7 15 9 12 8 12 10 9 7 12 9 9 + 10 P x - 3 P x - 9 P x + 8 P x + P x - 12 P x - P x 6 12 8 9 7 9 6 9 5 9 7 6 4 9 + 3 P x + 3 P x - 12 P x + 11 P x - 3 P x - 3 P x + 3 P x 6 6 5 6 4 6 3 6 4 3 3 3 2 3 3 + 3 P x - 3 P x + 7 P x - 3 P x + 3 P x - 3 P x + P x - P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 1, 3 r + 3}, {3 r + 1, 3 r + 2, 3 r + 3} P - 1 = 0 ---------------------------- (A,B)= , {3 r + 2, 3 r + 3}, {} 4 3 3 3 P x - P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 2, 3 r + 3}, {3 r + 1} 20 30 19 30 19 27 18 27 17 27 17 26 16 27 P x - P x - P x + P x - 3 P x - P x + 3 P x 16 26 17 24 16 24 16 23 15 24 15 23 + 3 P x - 3 P x + 7 P x + 3 P x - P x - 4 P x 14 24 16 21 14 23 13 24 15 21 14 22 + 2 P x + 3 P x + 2 P x - 2 P x - 3 P x - P x 13 23 14 21 14 20 13 21 13 20 12 21 - 3 P x + 10 P x + 2 P x - 9 P x - 12 P x + 3 P x 14 18 12 20 11 21 13 18 12 19 11 20 + 3 P x + 4 P x - P x - 11 P x + 4 P x - P x 10 21 13 17 12 18 12 17 11 18 13 15 + P x - 3 P x + 8 P x + 5 P x - 8 P x - 3 P x 11 17 10 18 12 15 10 17 9 18 11 15 - 7 P x + 5 P x + 3 P x + 6 P x - P x - 9 P x 10 16 9 17 11 14 10 15 10 14 9 15 + 10 P x - P x - P x + 8 P x + 12 P x - 8 P x 11 12 9 14 8 15 10 12 8 14 7 15 - P x - 7 P x + 3 P x + 10 P x + 4 P x - 2 P x 9 12 8 13 7 14 9 11 8 12 10 9 8 11 - 9 P x + 4 P x - 3 P x - P x + 8 P x + P x + 5 P x 7 12 9 9 7 11 6 12 8 9 6 11 7 9 - 9 P x - P x - 12 P x + 2 P x + 3 P x + 2 P x - 11 P x 6 10 7 8 6 9 6 8 5 9 7 6 5 8 - P x - 3 P x + 10 P x + 2 P x - P x - 3 P x - 4 P x 4 9 6 6 4 8 5 6 4 6 4 5 3 6 + 3 P x + 3 P x + 3 P x - 3 P x + 7 P x + 3 P x - 3 P x 3 5 4 3 3 3 2 3 3 - P x + 3 P x - 3 P x + P x - P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 2, 3 r + 3}, {3 r + 2} 20 30 19 30 19 28 19 27 18 27 17 27 16 27 P x - P x + P x - P x + P x - 3 P x + 3 P x 17 25 17 24 16 25 16 24 16 23 15 24 + 3 P x - 3 P x - 6 P x + 6 P x + 3 P x - P x 16 22 14 24 16 21 15 22 13 24 15 21 - 6 P x + 2 P x + 3 P x + 3 P x - 2 P x - 3 P x 14 22 14 21 13 22 14 20 13 21 14 19 - 5 P x + 8 P x + 7 P x + 3 P x - 9 P x - 6 P x 13 20 12 21 14 18 13 19 11 21 13 18 - 8 P x + 3 P x + 3 P x + 19 P x - P x - 8 P x 12 19 10 21 13 17 12 18 11 19 13 16 - 6 P x + P x - 9 P x + 9 P x + 3 P x + 9 P x 12 17 11 18 10 19 13 15 12 16 11 17 + 3 P x - 8 P x - 4 P x - 3 P x - 6 P x - 3 P x 10 18 12 15 11 16 10 17 9 18 11 15 + 5 P x + 3 P x + 12 P x + 6 P x - P x - 8 P x 10 16 11 14 10 15 9 16 11 13 10 14 - 18 P x - 3 P x + 8 P x + 3 P x + 3 P x + 18 P x 9 15 11 12 10 13 9 14 8 15 10 12 - 8 P x - P x - 23 P x - 3 P x + 3 P x + 6 P x 9 13 7 15 10 11 9 12 8 13 10 10 + 12 P x - 2 P x + 6 P x - 8 P x - 6 P x - 4 P x 9 11 8 12 7 13 10 9 9 10 8 11 7 12 - 3 P x + 9 P x + 7 P x + P x + 3 P x + 3 P x - 9 P x 9 9 8 10 7 11 6 12 8 9 7 10 7 9 - P x - 6 P x - 8 P x + 2 P x + 3 P x + 19 P x - 8 P x 6 10 7 8 6 9 7 7 6 8 5 9 7 6 - 5 P x - 9 P x + 8 P x + 9 P x + 3 P x - P x - 3 P x 6 7 4 9 6 6 5 7 5 6 4 7 4 6 - 6 P x + 3 P x + 3 P x + 3 P x - 3 P x - 6 P x + 6 P x 4 5 3 6 4 4 4 3 3 4 3 3 2 3 3 + 3 P x - 3 P x - 6 P x + 3 P x + 3 P x - 3 P x + P x - P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 2, 3 r + 3}, {3 r + 3} 20 30 19 30 19 28 19 27 18 27 17 27 16 27 P x - P x + P x - P x + P x - 3 P x + 3 P x 17 25 17 24 16 25 16 24 16 23 15 24 + 3 P x - 3 P x - 6 P x + 7 P x + 3 P x - 3 P x 16 22 14 24 16 21 15 22 13 24 15 21 - 6 P x + 3 P x + 3 P x + 3 P x - 3 P x - 3 P x 14 22 14 21 13 22 14 20 13 21 14 19 - 6 P x + 11 P x + 9 P x + 3 P x - 12 P x - 6 P x 13 20 12 21 14 18 13 19 11 21 13 18 - 9 P x + 3 P x + 3 P x + 21 P x - P x - 9 P x 12 19 10 21 13 17 12 18 11 19 13 16 - 6 P x + P x - 9 P x + 8 P x + 3 P x + 9 P x 12 17 11 18 10 19 13 15 12 16 11 17 + 3 P x - 9 P x - 4 P x - 3 P x - 6 P x - 3 P x 10 18 12 15 11 16 10 17 9 18 11 15 + 10 P x + 3 P x + 12 P x + 6 P x - P x - 8 P x 10 16 11 14 10 15 9 16 11 13 10 14 - 24 P x - 3 P x + 10 P x + 3 P x + 3 P x + 18 P x 9 15 11 12 10 13 9 14 8 15 10 12 - 9 P x - P x - 23 P x - 3 P x + 3 P x + 6 P x 9 13 7 15 10 11 9 12 8 13 10 10 + 12 P x - 3 P x + 6 P x - 8 P x - 6 P x - 4 P x 9 11 8 12 7 13 10 9 9 10 8 11 - 3 P x + 8 P x + 9 P x + P x + 3 P x + 3 P x 7 12 9 9 8 10 7 11 6 12 8 9 7 10 - 12 P x - P x - 6 P x - 9 P x + 3 P x + 3 P x + 21 P x 7 9 6 10 7 8 6 9 7 7 6 8 5 9 - 9 P x - 6 P x - 9 P x + 11 P x + 9 P x + 3 P x - 3 P x 7 6 6 7 4 9 6 6 5 7 5 6 4 7 - 3 P x - 6 P x + 3 P x + 3 P x + 3 P x - 3 P x - 6 P x 4 6 4 5 3 6 4 4 4 3 3 4 3 3 + 7 P x + 3 P x - 3 P x - 6 P x + 3 P x + 3 P x - 3 P x 2 3 3 + P x - P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 2, 3 r + 3}, {3 r + 1, 3 r + 2} 20 30 19 30 19 27 18 27 17 27 16 27 17 24 P x - P x - P x + P x - 3 P x + 3 P x - 3 P x 16 24 15 24 14 24 16 21 13 24 15 21 + 6 P x - P x + 2 P x + 3 P x - 2 P x - 3 P x 14 21 13 21 12 21 14 18 11 21 13 18 + 8 P x - 9 P x + 3 P x + 3 P x - P x - 11 P x 10 21 12 18 11 18 13 15 10 18 12 15 + P x + 9 P x - 8 P x - 3 P x + 5 P x + 3 P x 9 18 11 15 10 15 9 15 11 12 8 15 - P x - 9 P x + 12 P x - 8 P x - P x + 3 P x 10 12 7 15 9 12 8 12 10 9 7 12 9 9 + 10 P x - 2 P x - 9 P x + 9 P x + P x - 9 P x - P x 6 12 8 9 7 9 6 9 5 9 7 6 4 9 + 2 P x + 3 P x - 11 P x + 8 P x - P x - 3 P x + 3 P x 6 6 5 6 4 6 3 6 4 3 3 3 2 3 3 + 3 P x - 3 P x + 6 P x - 3 P x + 3 P x - 3 P x + P x - P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 2, 3 r + 3}, {3 r + 1, 3 r + 3} 20 30 19 30 19 27 18 27 17 27 16 27 17 24 P x - P x - P x + P x - 3 P x + 3 P x - 3 P x 16 24 15 24 14 24 16 21 13 24 15 21 + 7 P x - 3 P x + 3 P x + 3 P x - 3 P x - 3 P x 14 21 13 21 12 21 14 18 11 21 13 18 + 11 P x - 12 P x + 3 P x + 3 P x - P x - 12 P x 10 21 12 18 11 18 13 15 10 18 12 15 + P x + 8 P x - 9 P x - 3 P x + 10 P x + 3 P x 9 18 11 15 10 15 9 15 11 12 8 15 - P x - 9 P x + 14 P x - 9 P x - P x + 3 P x 10 12 7 15 9 12 8 12 10 9 7 12 9 9 + 10 P x - 3 P x - 9 P x + 8 P x + P x - 12 P x - P x 6 12 8 9 7 9 6 9 5 9 7 6 4 9 + 3 P x + 3 P x - 12 P x + 11 P x - 3 P x - 3 P x + 3 P x 6 6 5 6 4 6 3 6 4 3 3 3 2 3 3 + 3 P x - 3 P x + 7 P x - 3 P x + 3 P x - 3 P x + P x - P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 2, 3 r + 3}, {3 r + 2, 3 r + 3} 2 3 3 P x - P x + P x - P + 1 = 0 ---------------------------- (A,B)= , {3 r + 2, 3 r + 3}, {3 r + 1, 3 r + 2, 3 r + 3} P - 1 = 0 ---------------------------- (A,B)= , {3 r + 1, 3 r + 2, 3 r + 3}, {} P - 1 = 0 ---------------------------- (A,B)= , {3 r + 1, 3 r + 2, 3 r + 3}, {3 r + 1} P - 1 = 0 ---------------------------- (A,B)= , {3 r + 1, 3 r + 2, 3 r + 3}, {3 r + 2} P - 1 = 0 ---------------------------- (A,B)= , {3 r + 1, 3 r + 2, 3 r + 3}, {3 r + 3} P - 1 = 0 ---------------------------- (A,B)= , {3 r + 1, 3 r + 2, 3 r + 3}, {3 r + 1, 3 r + 2} P - 1 = 0 ---------------------------- (A,B)= , {3 r + 1, 3 r + 2, 3 r + 3}, {3 r + 1, 3 r + 3} P - 1 = 0 ---------------------------- (A,B)= , {3 r + 1, 3 r + 2, 3 r + 3}, {3 r + 2, 3 r + 3} P - 1 = 0 ---------------------------- (A,B)= , {3 r + 1, 3 r + 2, 3 r + 3}, {3 r + 1, 3 r + 2, 3 r + 3} P - 1 = 0 ------------------------- This took, 354687.430, second.