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

16, 744, 50354, 2462064, 139472532, 7621612496, 420570135944, 23122750594160, 1272913614363472, 70046421764651488, 3855022666171830728, 212153410644220498768, 11675594777180367650512, 642548778638303396036528, 35361754611803652243506632, 1946082778374581215370587632

Offset: 2

Author

Seiichi Manyama, Nov 27 2020

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 2..400
• Vaclav Kotesovec, Empirical g.f.
• Eric Weisstein's World of Mathematics, Hamiltonian Cycle
• Eric Weisstein's World of Mathematics, King Graph
• Index entries for sequences related to graphs, Hamiltonian

Crossrefs

Column 5 of A339190.

Cf. A339199.

Programs

Python

# Using graphillion
from graphillion import GraphSet
def make_nXk_king_graph(n, k):
    grids = []
    for i in range(1, k + 1):
        for j in range(1, n):
            grids.append((i + (j - 1) * k, i + j * k))
            if i < k:
                grids.append((i + (j - 1) * k, i + j * k + 1))
            if i > 1:
                grids.append((i + (j - 1) * k, i + j * k - 1))
    for i in range(1, k * n, k):
        for j in range(1, k):
            grids.append((i + j - 1, i + j))
    return grids
def A339190(n, k):
    universe = make_nXk_king_graph(n, k)
    GraphSet.set_universe(universe)
    cycles = GraphSet.cycles(is_hamilton=True)
    return cycles.len()
def A339202(n):
    return A339190(n, 5)
print([A339202(n) for n in range(2, 20)])