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A338617 Number of spanning trees in the n X 4 king graph. 2
1, 2304, 1612127, 1064918960, 698512774464, 457753027631164, 299940605530116319, 196531575367664678400, 128774089577828985307985, 84377085408032081020147412, 55286683084713553039968700608, 36225680193828279388607070447232, 23736274839549237072891352060244017 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..300

Eric Weisstein's World of Mathematics, King Graph

Eric Weisstein's World of Mathematics, Spanning Tree

FORMULA

Empirical g.f.: x*(56*x^7 + 7072*x^6 - 162708*x^5 + 371791*x^4 + 18080*x^3 - 49920*x^2 + 1556*x + 1) / (x^8 - 748*x^7 + 61345*x^6 - 368764*x^5 + 680848*x^4 - 368764*x^3 + 61345*x^2 - 748*x + 1). - Vaclav Kotesovec, Dec 04 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 A338029(n, k):

    if n == 1 or k == 1: return 1

    universe = make_nXk_king_graph(n, k)

    GraphSet.set_universe(universe)

    spanning_trees = GraphSet.trees(is_spanning=True)

    return spanning_trees.len()

def A338617(n):

    return A338029(n, 4)

print([A338617(n) for n in range(1, 20)])

CROSSREFS

Column 4 of A338029.

Cf. A003696.

Sequence in context: A259321 A223302 A174558 * A274578 A031774 A031546

Adjacent sequences:  A338614 A338615 A338616 * A338618 A338619 A338620

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Nov 29 2020

STATUS

approved

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Last modified October 3 02:59 EDT 2022. Contains 357230 sequences. (Running on oeis4.)