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A296527 Number of (undirected) cycles in the n X n torus grid graph.

%I A296527 #23 Feb 16 2025 08:33:52
%S A296527 312,14704,2183490,995818716,1383238940818,5846378997135040,
%T A296527 75162787766308673244
%N A296527 Number of (undirected) cycles in the n X n torus grid graph.
%H A296527 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>.
%H A296527 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TorusGridGraph.html">Torus Grid Graph</a>.
%t A296527 Table[Length[FindCycle[GraphProduct[CycleGraph[n], CycleGraph[n], "Cartesian"], Infinity, All]], {n, 3, 5}] (* _Eric W. Weisstein_, Dec 16 2023 *)
%o A296527 (Python)
%o A296527 # Using graphillion
%o A296527 from graphillion import GraphSet
%o A296527 def make_CnXCk(n, k):
%o A296527     grids = []
%o A296527     for i in range(1, k + 1):
%o A296527         for j in range(1, n):
%o A296527             grids.append((i + (j - 1) * k, i + j * k))
%o A296527         grids.append((i + (n - 1) * k, i))
%o A296527     for i in range(1, k * n, k):
%o A296527         for j in range(1, k):
%o A296527             grids.append((i + j - 1, i + j))
%o A296527         grids.append((i + k - 1, i))
%o A296527     return grids
%o A296527 def A296527(n):
%o A296527     universe = make_CnXCk(n, n)
%o A296527     GraphSet.set_universe(universe)
%o A296527     cycles = GraphSet.cycles()
%o A296527     return cycles.len()
%o A296527 print([A296527(n) for n in range(3, 7)])  # _Seiichi Manyama_, Nov 22 2020
%Y A296527 Cf. A222199, A268838.
%K A296527 nonn,more
%O A296527 3,1
%A A296527 _Eric W. Weisstein_, Dec 14 2017
%E A296527 a(7) from _Andrew Howroyd_, Dec 14 2017
%E A296527 a(8)-a(9) from _Ed Wynn_, Jun 28 2023