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 A339797 Number of (undirected) Hamiltonian paths in the graph C_3 X C_n. 5
 756, 4128, 18240, 73368, 277536, 1001760, 3512160, 12009480, 40390944, 133893936, 439304736, 1428450072, 4613176800, 14809528896, 47315578848, 150534443304, 477237381024, 1508232832080, 4753573999776, 14945425070136, 46886868887136, 146802927436128, 458818252975200 (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, Hamiltonian Path 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, is_hamilton=True) 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 A339797(n): return B(n, 3) print([A339797(n) for n in range(3, 10)]) CROSSREFS Cf. A003685, A268838, A339795, A339798. Sequence in context: A158657 A004010 A320686 * A288779 A018898 A004048 Adjacent sequences: A339794 A339795 A339796 * A339798 A339799 A339800 KEYWORD nonn AUTHOR Seiichi Manyama, Dec 17 2020 STATUS approved

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Last modified February 2 09:12 EST 2023. Contains 360003 sequences. (Running on oeis4.)