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A339197 Number of (undirected) cycles on the n X 3 king graph. 3
30, 348, 3459, 33145, 316164, 3013590, 28722567, 273751765, 2609096478, 24866992602, 237004387635, 2258860992595, 21528938911842, 205189789087374, 1955639788756293, 18638973217791295, 177645865363829526, 1693121885638023396, 16136945905019298321, 153799336805212613275 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 16 02:14 EDT 2021. Contains 345055 sequences. (Running on oeis4.)