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%I #16 Dec 09 2020 05:37:14
%S 204,33145,4847163,545217435,61575093671,7050330616441,
%T 808723201743855,92672075290059017,10617254793634907021,
%U 1216460857186123433837,139377550879455782939427,15969325570952770252910697,1829698785056144504575785405,209639263869115933534540710701
%N Number of (undirected) cycles on the n X 5 king graph.
%H Seiichi Manyama, <a href="/A339199/b339199.txt">Table of n, a(n) for n = 2..400</a>
%H Vaclav Kotesovec, <a href="/A339199/a339199.txt">Empirical g.f.</a>
%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/KingGraph.html">King Graph</a>
%o (Python)
%o # Using graphillion
%o from graphillion import GraphSet
%o def make_nXk_king_graph(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 if i < k:
%o grids.append((i + (j - 1) * k, i + j * k + 1))
%o if i > 1:
%o grids.append((i + (j - 1) * k, i + j * k - 1))
%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 return grids
%o def A339098(n, k):
%o universe = make_nXk_king_graph(n, k)
%o GraphSet.set_universe(universe)
%o cycles = GraphSet.cycles()
%o return cycles.len()
%o def A339199(n):
%o return A339098(n, 5)
%o print([A339199(n) for n in range(2, 20)])
%Y Column 5 of A339098.
%Y Cf. A339202.
%K nonn
%O 2,1
%A _Seiichi Manyama_, Nov 27 2020
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