A339197 Number of (undirected) cycles on the n X 3 king graph.

30, 348, 3459, 33145, 316164, 3013590, 28722567, 273751765, 2609096478, 24866992602, 237004387635, 2258860992595, 21528938911842, 205189789087374, 1955639788756293, 18638973217791295, 177645865363829526, 1693121885638023396, 16136945905019298321, 153799336805212613275

Offset

2,1

Links

Seiichi Manyama, Table of n, a(n) for n = 2..1000

Eric Weisstein's World of Mathematics, Graph Cycle

Eric Weisstein's World of Mathematics, King Graph

Formula

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

Prog

(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 A339197(n):
    return A339098(n, 3)
print([A339197(n) for n in range(2, 30)])

Crossrefs

Column 3 of A339098.

Cf. A339200.

Sequence in context: A115500 A214085 A125418 * A107916 A091775 A222086

Adjacent sequences: A339194 A339195 A339196 * A339198 A339199 A339200

Keyword

nonn

Author

Seiichi Manyama, Nov 27 2020

Status

approved