A339199 - OEIS

%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