%I #13 Dec 09 2020 04:51:32
%S 30,348,3459,33145,316164,3013590,28722567,273751765,2609096478,
%T 24866992602,237004387635,2258860992595,21528938911842,
%U 205189789087374,1955639788756293,18638973217791295,177645865363829526,1693121885638023396,16136945905019298321,153799336805212613275
%N Number of (undirected) cycles on the n X 3 king graph.
%H Seiichi Manyama, <a href="/A339197/b339197.txt">Table of n, a(n) for n = 2..1000</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>
%F Empirical g.f.: -x^2 * (11*x^4 + 49*x^3 + 69*x^2 + 48*x + 30) / ((x-1)^2 * (6*x^4 + 5*x^3 + 14*x^2 + 8*x - 1)). - _Vaclav Kotesovec_, Dec 09 2020
%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 A339197(n):
%o return A339098(n, 3)
%o print([A339197(n) for n in range(2, 30)])
%Y Column 3 of A339098.
%Y Cf. A339200.
%K nonn
%O 2,1
%A _Seiichi Manyama_, Nov 27 2020