A339137 - OEIS

%I #15 Dec 09 2020 04:39:38

%S 1,28,225,1540,10217,67388,444017,2925140,19270105,126946444,

%T 836290209,5509263332,36293601737,239092863324,1575081964113,

%U 10376232739316,68355938510649,450311249502892,2966534083948417,19542759549039748,128742647137776169,848123272992954492

%N Number of (undirected) cycles in the graph C_4 X P_n.

%H Seiichi Manyama, <a href="/A339137/b339137.txt">Table of n, a(n) for n = 1..1000</a>

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

%F Empirical g.f.: -x*(6*x^3+29*x^2-18*x-1) / ((x-1)^2 * (2*x^3+9*x^2-8*x+1)). - _Vaclav Kotesovec_, Dec 09 2020

%o (Python)

%o # Using graphillion

%o from graphillion import GraphSet

%o def make_CnXPk(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         grids.append((i + (n - 1) * k, i))

%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 A339137(n):

%o     universe = make_CnXPk(4, n)

%o     GraphSet.set_universe(universe)

%o     cycles = GraphSet.cycles()

%o     return cycles.len()

%o print([A339137(n) for n in range(1, 20)])

%Y Cf. A003699 (Hamiltonian cycles), A288637, A339075, A339136, A339140, A339142, A339143.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Nov 25 2020