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 A338297 Number of Hamiltonian paths in C_6 X P_n. 1
 6, 228, 4800, 76116, 1094316, 14557092, 183735204, 2230289220, 26275912776, 302338568832, 3412921463352, 37923555328200, 415863933818988, 4509400849281240, 48428461587426108, 515767225814395500, 5452991323044249720, 57282647077608267072, 598324561437126968664, 6217929367753246782612 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Seiichi Manyama, Table of n, a(n) for n = 1..25 PROG (Python) # Using graphillion from graphillion import GraphSet def make_CnXPk(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)) return grids def A(start, goal, n, k): universe = make_CnXPk(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 A338297(n): return B(6, n) print([A338297(n) for n in range(1, 11)]) CROSSREFS Cf. A003689 (C_3 X P_n), A003752 (C_4 X P_n), A003732 (C_5 X P_n), A268894 (C_n X P_n). Cf. A180582, A339143, A338962. Sequence in context: A166502 A173083 A366252 * A084070 A282736 A277293 Adjacent sequences: A338294 A338295 A338296 * A338298 A338299 A338300 KEYWORD nonn AUTHOR Seiichi Manyama, Dec 18 2020 STATUS approved

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Last modified August 12 19:26 EDT 2024. Contains 375113 sequences. (Running on oeis4.)