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 A339200 Number of (undirected) Hamiltonian cycles on the n X 3 king graph. 4
 4, 16, 120, 744, 4922, 31904, 208118, 1354872, 8826022, 57483536, 374412158, 2438639080, 15883563110, 103454037120, 673825180718, 4388811619032, 28585557862518, 186185731404016, 1212679737590398, 7898522254036168, 51445284278407878, 335077523213321312, 2182453613487235150, 14214930709900240312 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 LINKS Seiichi Manyama, Table of n, a(n) for n = 2..1000 Eric Weisstein's World of Mathematics, Hamiltonian Cycle Eric Weisstein's World of Mathematics, King Graph FORMULA Empirical g.f.: 2*x^2 * (3*x^4 + 4*x^3 + 2*x^2 - 2) / (6*x^4 + 8*x^3 + 15*x^2 + 4*x - 1). - Vaclav Kotesovec, Dec 09 2020 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() def A339200(n):     return A339190(n, 3) print([A339200(n) for n in range(2, 20)]) CROSSREFS Column 3 of A339190. Cf. A339197. Sequence in context: A332752 A210573 A337040 * A087335 A204573 A306561 Adjacent sequences:  A339197 A339198 A339199 * A339201 A339202 A339203 KEYWORD nonn AUTHOR Seiichi Manyama, Nov 27 2020 STATUS approved

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Last modified June 24 01:07 EDT 2021. Contains 345404 sequences. (Running on oeis4.)