A339137 Number of (undirected) cycles in the graph C_4 X P_n.

1, 28, 225, 1540, 10217, 67388, 444017, 2925140, 19270105, 126946444, 836290209, 5509263332, 36293601737, 239092863324, 1575081964113, 10376232739316, 68355938510649, 450311249502892, 2966534083948417, 19542759549039748, 128742647137776169, 848123272992954492

Offset: 1

Author

Seiichi Manyama, Nov 25 2020

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Graph Cycle

Crossrefs

Cf. A003699 (Hamiltonian cycles), A288637, A339075, A339136, A339140, A339142, A339143.

Programs

Python

# Using graphillion
from graphillion import GraphSet
def make_CnXPk(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))
    return grids
def A339137(n):
    universe = make_CnXPk(4, n)
    GraphSet.set_universe(universe)
    cycles = GraphSet.cycles()
    return cycles.len()
print([A339137(n) for n in range(1, 20)])

Formula

Empirical g.f.: -x*(6*x^3+29*x^2-18*x-1) / ((x-1)^2 * (2*x^3+9*x^2-8*x+1)). - Vaclav Kotesovec, Dec 09 2020