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 A339190 Square array T(n,k), n >= 2, k >= 2, read by antidiagonals, where T(n,k) is the number of (undirected) Hamiltonian cycles on the n X k king graph. 6
 3, 4, 4, 8, 16, 8, 16, 120, 120, 16, 32, 744, 2830, 744, 32, 64, 4922, 50354, 50354, 4922, 64, 128, 31904, 1003218, 2462064, 1003218, 31904, 128, 256, 208118, 19380610, 139472532, 139472532, 19380610, 208118, 256, 512, 1354872, 378005474, 7621612496, 22853860116, 7621612496, 378005474, 1354872, 512 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 LINKS Seiichi Manyama, Antidiagonals n = 2..12, flattened Eric Weisstein's World of Mathematics, Hamiltonian Cycle Eric Weisstein's World of Mathematics, King Graph FORMULA T(n,k) = T(k,n). EXAMPLE Square array T(n,k) begins:    3,     4,        8,         16,            32,               64, ...    4,    16,      120,        744,          4922,            31904, ...    8,   120,     2830,      50354,       1003218,         19380610, ...   16,   744,    50354,    2462064,     139472532,       7621612496, ...   32,  4922,  1003218,  139472532,   22853860116,    3601249330324, ...   64, 31904, 19380610, 7621612496, 3601249330324, 1622043117414624, ... 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 A339190(n, k):     universe = make_nXk_king_graph(n, k)     GraphSet.set_universe(universe)     cycles = GraphSet.cycles(is_hamilton=True)     return cycles.len() print([A339190(j + 2, i - j + 2) for i in range(10 - 1) for j in range(i + 1)]) CROSSREFS Rows and columns 3..5 give A339200, A339201, A339202. Main diagonal gives A140519. Cf. A321172, A339098, A339849. Sequence in context: A075550 A292729 A328989 * A137529 A245258 A086180 Adjacent sequences:  A339187 A339188 A339189 * A339191 A339192 A339193 KEYWORD nonn,tabl AUTHOR Seiichi Manyama, Nov 27 2020 STATUS approved

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Last modified May 6 14:16 EDT 2021. Contains 343586 sequences. (Running on oeis4.)