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%I #22 Dec 30 2023 13:17:46
%S 312,14704,2183490,995818716,1383238940818,5846378997135040,
%T 75162787766308673244
%N Number of (undirected) cycles in the n X n torus grid graph.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TorusGridGraph.html">Torus Grid Graph</a>.
%t Table[Length[FindCycle[GraphProduct[CycleGraph[n], CycleGraph[n], "Cartesian"], Infinity, All]], {n, 3, 5}] (* _Eric W. Weisstein_, Dec 16 2023 *)
%o (Python)
%o # Using graphillion
%o from graphillion import GraphSet
%o def make_CnXCk(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 grids.append((i + k - 1, i))
%o return grids
%o def A296527(n):
%o universe = make_CnXCk(n, n)
%o GraphSet.set_universe(universe)
%o cycles = GraphSet.cycles()
%o return cycles.len()
%o print([A296527(n) for n in range(3, 7)]) # _Seiichi Manyama_, Nov 22 2020
%Y Cf. A222199, A268838.
%K nonn,more
%O 3,1
%A _Eric W. Weisstein_, Dec 14 2017
%E a(7) from _Andrew Howroyd_, Dec 14 2017
%E a(8)-a(9) from _Ed Wynn_, Jun 28 2023
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