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A339196 Number of (undirected) cycles on the n X 2 king graph. 2
7, 30, 85, 204, 451, 954, 1969, 4008, 8095, 16278, 32653, 65412, 130939, 262002, 524137, 1048416, 2096983, 4194126, 8388421, 16777020, 33554227, 67108650, 134217505, 268435224, 536870671, 1073741574, 2147483389, 4294967028, 8589934315, 17179868898, 34359738073, 68719476432 (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 * (7 + 2*x) / ((-1 + x)^2 * (-1 + 2*x)). - 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 A339196(n):

    return A339098(n, 2)

print([A339196(n) for n in range(2, 30)])

CROSSREFS

Column 2 of A339098.

Sequence in context: A083474 A030440 A256225 * A232093 A045889 A038739

Adjacent sequences:  A339193 A339194 A339195 * A339197 A339198 A339199

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.)