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 A339795 Number of (undirected) paths in the graph C_3 X C_n. 5
 4536, 41676, 324570, 2298906, 15340836, 98401032, 614180286, 3759485910, 22684148388, 135385868268, 801141412422, 4708188092034, 27512477620020, 160001531341584, 926684449543278, 5347897587948078, 30765345147232932, 176489253686952180, 1009897820473377654 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 LINKS Seiichi Manyama, Table of n, a(n) for n = 3..50 Eric Weisstein's World of Mathematics, Torus Grid Graph PROG (Python) # Using graphillion from graphillion import GraphSet def make_CnXCk(n, k): grids = [] for i in range(1, k + 1): for j in range(1, n): grids.append((i + (j - 1) * k, i + j * k)) grids.append((i + (n - 1) * k, i)) for i in range(1, k * n, k): for j in range(1, k): grids.append((i + j - 1, i + j)) grids.append((i + k - 1, i)) return grids def A(start, goal, n, k): universe = make_CnXCk(n, k) GraphSet.set_universe(universe) paths = GraphSet.paths(start, goal) return paths.len() def B(n, k): m = k * n s = 0 for i in range(1, m): for j in range(i + 1, m + 1): s += A(i, j, n, k) return s def A339795(n): return B(n, 3) print([A339795(n) for n in range(3, 10)]) CROSSREFS Cf. A307919, A339796, A358869, A358872. Cf. A339074, A339797 (Hamiltonian paths). Sequence in context: A235852 A138731 A250450 * A337314 A234171 A262848 Adjacent sequences: A339792 A339793 A339794 * A339796 A339797 A339798 KEYWORD nonn AUTHOR Seiichi Manyama, Dec 17 2020 STATUS approved

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Last modified March 23 19:33 EDT 2023. Contains 361450 sequences. (Running on oeis4.)