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A339074 Number of (undirected) cycles in the graph C_3 X C_n.

%I A339074 #15 Feb 16 2025 08:34:01
%S A339074 312,1531,7298,35205,174268,885719,4601982,24306577,129851384,
%T A339074 698930787,3780126106,20505863069,111441343860,606312668335,
%U A339074 3300926292470,17978225967081,97939845566896,533619551723963,2907629293865874,15844069824657013,86338863686763692,470492593924667271
%N A339074 Number of (undirected) cycles in the graph C_3 X C_n.
%H A339074 Seiichi Manyama, <a href="/A339074/b339074.txt">Table of n, a(n) for n = 3..500</a>
%H A339074 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%H A339074 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TorusGridGraph.html">Torus Grid Graph</a>
%o A339074 (Python)
%o A339074 # Using graphillion
%o A339074 from graphillion import GraphSet
%o A339074 def make_CnXCk(n, k):
%o A339074     grids = []
%o A339074     for i in range(1, k + 1):
%o A339074         for j in range(1, n):
%o A339074             grids.append((i + (j - 1) * k, i + j * k))
%o A339074         grids.append((i + (n - 1) * k, i))
%o A339074     for i in range(1, k * n, k):
%o A339074         for j in range(1, k):
%o A339074             grids.append((i + j - 1, i + j))
%o A339074         grids.append((i + k - 1, i))
%o A339074     return grids
%o A339074 def A339074(n):
%o A339074     universe = make_CnXCk(n, 3)
%o A339074     GraphSet.set_universe(universe)
%o A339074     cycles = GraphSet.cycles()
%o A339074     return cycles.len()
%o A339074 print([A339074(n) for n in range(3, 30)])
%Y A339074 Cf. A194952, A296527, A339075.
%K A339074 nonn
%O A339074 3,1
%A A339074 _Seiichi Manyama_, Nov 22 2020