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A339142 Number of (undirected) cycles in the graph C_5 X P_n.

%I A339142 #16 Feb 16 2025 08:34:01
%S A339142 1,52,733,9394,119235,1512196,19177677,243212478,3084441599,
%T A339142 39117172360,496087629441,6291429718962,79788500460003,
%U A339142 1011885230273244,12832823194696645,162747064808635206,2063973507784856167,26175505197898511728,331960206747350288969,4209950410912939269210
%N A339142 Number of (undirected) cycles in the graph C_5 X P_n.
%H A339142 Ed Wynn, <a href="/A339142/b339142.txt">Table of n, a(n) for n = 1..87</a>
%H A339142 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%o A339142 (Python)
%o A339142 # Using graphillion
%o A339142 from graphillion import GraphSet
%o A339142 def make_CnXPk(n, k):
%o A339142     grids = []
%o A339142     for i in range(1, k + 1):
%o A339142         for j in range(1, n):
%o A339142             grids.append((i + (j - 1) * k, i + j * k))
%o A339142         grids.append((i + (n - 1) * k, i))
%o A339142     for i in range(1, k * n, k):
%o A339142         for j in range(1, k):
%o A339142             grids.append((i + j - 1, i + j))
%o A339142     return grids
%o A339142 def A339142(n):
%o A339142     universe = make_CnXPk(5, n)
%o A339142     GraphSet.set_universe(universe)
%o A339142     cycles = GraphSet.cycles()
%o A339142     return cycles.len()
%o A339142 print([A339142(n) for n in range(1, 9)])
%Y A339142 Cf. A003731 (Hamiltonian cycles), A339117, A339136, A339137, A339140, A339143.
%K A339142 nonn
%O A339142 1,2
%A A339142 _Seiichi Manyama_, Nov 25 2020
%E A339142 More terms from _Ed Wynn_, Jun 28 2023