A339199 Number of (undirected) cycles on the n X 5 king graph.

204, 33145, 4847163, 545217435, 61575093671, 7050330616441, 808723201743855, 92672075290059017, 10617254793634907021, 1216460857186123433837, 139377550879455782939427, 15969325570952770252910697, 1829698785056144504575785405, 209639263869115933534540710701

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, Graph Cycle
• Eric Weisstein's World of Mathematics, King Graph

Crossrefs

Column 5 of A339098.

Cf. A339202.

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 A339098(n, k):
    universe = make_nXk_king_graph(n, k)
    GraphSet.set_universe(universe)
    cycles = GraphSet.cycles()
    return cycles.len()
def A339199(n):
    return A339098(n, 5)
print([A339199(n) for n in range(2, 20)])