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A339199 Number of (undirected) cycles on the n X 5 king graph. 3
204, 33145, 4847163, 545217435, 61575093671, 7050330616441, 808723201743855, 92672075290059017, 10617254793634907021, 1216460857186123433837, 139377550879455782939427, 15969325570952770252910697, 1829698785056144504575785405, 209639263869115933534540710701 (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, Graph Cycle

Eric Weisstein's World of Mathematics, King Graph

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 A339199(n):

    return A339098(n, 5)

print([A339199(n) for n in range(2, 20)])

CROSSREFS

Column 5 of A339098.

Cf. A339202.

Sequence in context: A209790 A348603 A194192 * A263505 A270605 A072573

Adjacent sequences:  A339196 A339197 A339198 * A339200 A339201 A339202

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Nov 27 2020

STATUS

approved

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Last modified August 10 13:12 EDT 2022. Contains 356039 sequences. (Running on oeis4.)