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A339075 Number of (undirected) cycles in the graph C_4 X C_n.

%I A339075 #14 Feb 16 2025 08:34:01
%S A339075 1531,14704,132089,1165194,10254423,90693764,808627861,7276584222,
%T A339075 66085185907,605303076120,5585690299505,51868931553714,
%U A339075 484136128508431,4537416076416428,42662439747995981,402124615161547590,3797500862839734443,35913373920441057600,340000796575687888937
%N A339075 Number of (undirected) cycles in the graph C_4 X C_n.
%H A339075 Seiichi Manyama, <a href="/A339075/b339075.txt">Table of n, a(n) for n = 3..100</a>
%H A339075 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%H A339075 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TorusGridGraph.html">Torus Grid Graph</a>
%o A339075 (Python)
%o A339075 # Using graphillion
%o A339075 from graphillion import GraphSet
%o A339075 def make_CnXCk(n, k):
%o A339075     grids = []
%o A339075     for i in range(1, k + 1):
%o A339075         for j in range(1, n):
%o A339075             grids.append((i + (j - 1) * k, i + j * k))
%o A339075         grids.append((i + (n - 1) * k, i))
%o A339075     for i in range(1, k * n, k):
%o A339075         for j in range(1, k):
%o A339075             grids.append((i + j - 1, i + j))
%o A339075         grids.append((i + k - 1, i))
%o A339075     return grids
%o A339075 def A339075(n):
%o A339075     universe = make_CnXCk(4, n)
%o A339075     GraphSet.set_universe(universe)
%o A339075     cycles = GraphSet.cycles()
%o A339075     return cycles.len()
%o A339075 print([A339075(n) for n in range(3, 30)])
%Y A339075 Cf. A216588, A296527, A339074.
%K A339075 nonn
%O A339075 3,1
%A A339075 _Seiichi Manyama_, Nov 22 2020