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A339200 Number of (undirected) Hamiltonian cycles on the n X 3 king graph. 4

%I #15 Dec 09 2020 05:10:26

%S 4,16,120,744,4922,31904,208118,1354872,8826022,57483536,374412158,

%T 2438639080,15883563110,103454037120,673825180718,4388811619032,

%U 28585557862518,186185731404016,1212679737590398,7898522254036168,51445284278407878,335077523213321312,2182453613487235150,14214930709900240312

%N Number of (undirected) Hamiltonian cycles on the n X 3 king graph.

%H Seiichi Manyama, <a href="/A339200/b339200.txt">Table of n, a(n) for n = 2..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HamiltonianCycle.html">Hamiltonian Cycle</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/KingGraph.html">King Graph</a>

%H <a href="/index/Gra#graphs">Index entries for sequences related to graphs, Hamiltonian</a>

%F 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

%o (Python)

%o # Using graphillion

%o from graphillion import GraphSet

%o def make_nXk_king_graph(n, k):

%o grids = []

%o for i in range(1, k + 1):

%o for j in range(1, n):

%o grids.append((i + (j - 1) * k, i + j * k))

%o if i < k:

%o grids.append((i + (j - 1) * k, i + j * k + 1))

%o if i > 1:

%o grids.append((i + (j - 1) * k, i + j * k - 1))

%o for i in range(1, k * n, k):

%o for j in range(1, k):

%o grids.append((i + j - 1, i + j))

%o return grids

%o def A339190(n, k):

%o universe = make_nXk_king_graph(n, k)

%o GraphSet.set_universe(universe)

%o cycles = GraphSet.cycles(is_hamilton=True)

%o return cycles.len()

%o def A339200(n):

%o return A339190(n, 3)

%o print([A339200(n) for n in range(2, 20)])

%Y Column 3 of A339190.

%Y Cf. A339197.

%K nonn

%O 2,1

%A _Seiichi Manyama_, Nov 27 2020

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)