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 A339762 Number of (undirected) Hamiltonian paths in the 4 X n king graph. 4
 1, 208, 4678, 171592, 4743130, 132202038, 3461461060, 88405359072, 2197293738684, 53565801482634, 1284136961473864, 30365618160010650, 709700882866473654, 16422374051280905778, 376744989106882359402, 8578133199326578887346, 194030408441913214687458 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Eric Weisstein's World of Mathematics, Graph Path Eric Weisstein's World of Mathematics, King Graph PROG (Python) # Using graphillion from graphillion import GraphSet def make_nXk_king_graph(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))             if i < k:                 grids.append((i + (j - 1) * k, i + j * k + 1))             if i > 1:                 grids.append((i + (j - 1) * k, i + j * k - 1))     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_nXk_king_graph(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 A339762(n):     return B(n, 4) print([A339762(n) for n in range(1, 11)]) CROSSREFS Cf. A003695, A308129, A339760, A339761, A339763. Sequence in context: A172967 A343507 A231111 * A223252 A223610 A184276 Adjacent sequences:  A339759 A339760 A339761 * A339763 A339764 A339765 KEYWORD nonn AUTHOR Seiichi Manyama, Dec 16 2020 STATUS approved

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Last modified July 25 09:05 EDT 2021. Contains 346286 sequences. (Running on oeis4.)