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A339795 Number of (undirected) paths in the graph C_3 X C_n. 3
4536, 41676, 324570, 2298906, 15340836, 98401032, 614180286, 3759485910, 22684148388, 135385868268, 801141412422, 4708188092034, 27512477620020, 160001531341584, 926684449543278, 5347897587948078, 30765345147232932, 176489253686952180, 1009897820473377654 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

LINKS

Table of n, a(n) for n=3..21.

Eric Weisstein's World of Mathematics, Torus Grid Graph

PROG

(Python)

# Using graphillion

from graphillion import GraphSet

def make_CnXCk(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))

        grids.append((i + (n - 1) * k, i))

    for i in range(1, k * n, k):

        for j in range(1, k):

            grids.append((i + j - 1, i + j))

        grids.append((i + k - 1, i))

    return grids

def A(start, goal, n, k):

    universe = make_CnXCk(n, k)

    GraphSet.set_universe(universe)

    paths = GraphSet.paths(start, goal)

    return paths.len()

def B(n, k):

    m = k * n

    s = 0

    for i in range(1, m):

        for j in range(i + 1, m + 1):

            s += A(i, j, n, k)

    return s

def A339795(n):

    return B(n, 3)

print([A339795(n) for n in range(3, 10)])

CROSSREFS

Cf. A307919, A339074, A339796, A339797 (Hamiltonian paths).

Sequence in context: A235852 A138731 A250450 * A337314 A234171 A262848

Adjacent sequences:  A339792 A339793 A339794 * A339796 A339797 A339798

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Dec 17 2020

STATUS

approved

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Last modified December 3 17:09 EST 2021. Contains 349467 sequences. (Running on oeis4.)