cp's OEIS Frontend

A339202 Number of (undirected) Hamiltonian cycles on the n X 5 king graph.

%I A339202 #16 Feb 16 2025 08:34:01
%S A339202 16,744,50354,2462064,139472532,7621612496,420570135944,
%T A339202 23122750594160,1272913614363472,70046421764651488,
%U A339202 3855022666171830728,212153410644220498768,11675594777180367650512,642548778638303396036528,35361754611803652243506632,1946082778374581215370587632
%N A339202 Number of (undirected) Hamiltonian cycles on the n X 5 king graph.
%H A339202 Seiichi Manyama, <a href="/A339202/b339202.txt">Table of n, a(n) for n = 2..400</a>
%H A339202 Vaclav Kotesovec, <a href="/A339202/a339202.txt">Empirical g.f.</a>
%H A339202 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HamiltonianCycle.html">Hamiltonian Cycle</a>
%H A339202 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KingGraph.html">King Graph</a>
%H A339202 <a href="/index/Gra#graphs">Index entries for sequences related to graphs, Hamiltonian</a>
%o A339202 (Python)
%o A339202 # Using graphillion
%o A339202 from graphillion import GraphSet
%o A339202 def make_nXk_king_graph(n, k):
%o A339202     grids = []
%o A339202     for i in range(1, k + 1):
%o A339202         for j in range(1, n):
%o A339202             grids.append((i + (j - 1) * k, i + j * k))
%o A339202             if i < k:
%o A339202                 grids.append((i + (j - 1) * k, i + j * k + 1))
%o A339202             if i > 1:
%o A339202                 grids.append((i + (j - 1) * k, i + j * k - 1))
%o A339202     for i in range(1, k * n, k):
%o A339202         for j in range(1, k):
%o A339202             grids.append((i + j - 1, i + j))
%o A339202     return grids
%o A339202 def A339190(n, k):
%o A339202     universe = make_nXk_king_graph(n, k)
%o A339202     GraphSet.set_universe(universe)
%o A339202     cycles = GraphSet.cycles(is_hamilton=True)
%o A339202     return cycles.len()
%o A339202 def A339202(n):
%o A339202     return A339190(n, 5)
%o A339202 print([A339202(n) for n in range(2, 20)])
%Y A339202 Column 5 of A339190.
%Y A339202 Cf. A339199.
%K A339202 nonn
%O A339202 2,1
%A A339202 _Seiichi Manyama_, Nov 27 2020