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A339202 Number of (undirected) Hamiltonian cycles on the n X 5 king graph. 4
16, 744, 50354, 2462064, 139472532, 7621612496, 420570135944, 23122750594160, 1272913614363472, 70046421764651488, 3855022666171830728, 212153410644220498768, 11675594777180367650512, 642548778638303396036528, 35361754611803652243506632, 1946082778374581215370587632 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

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

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 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)])

CROSSREFS

Column 5 of A339190.

Cf. A339199.

Sequence in context: A209537 A086701 A218297 * A307923 A159375 A221527

Adjacent sequences:  A339199 A339200 A339201 * A339203 A339204 A339205

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Nov 27 2020

STATUS

approved

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Last modified June 22 15:13 EDT 2021. Contains 345383 sequences. (Running on oeis4.)