A339143 Number of (undirected) cycles in the graph C_6 X P_n.

1, 94, 2301, 53644, 1248517, 29059380, 676374187, 15743068612, 366430841199, 8528932801462, 198516848612143, 4620617865735414, 107548097901476485, 2503256858519071030, 58265046263626611537, 1356159518571223920304, 31565557014929042873017

Offset: 1

Author

Seiichi Manyama, Nov 25 2020

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..500
• Eric Weisstein's World of Mathematics, Graph Cycle

Crossrefs

Cf. A180582 (Hamiltonian cycles), A339118, A339136, A339137, A339140, A339142.

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 A339143(n):
    universe = make_CnXPk(6, n)
    GraphSet.set_universe(universe)
    cycles = GraphSet.cycles()
    return cycles.len()
print([A339143(n) for n in range(1, 20)])

Formula

Empirical g.f.: -x*(1 + 63*x - 418*x^2 + 287*x^3 + 840*x^4 + 1721*x^5 - 2540*x^6 + 3001*x^7 - 1149*x^8 - 544*x^9 + 90*x^10) / ((-1 + x)^2 * (-1 + 29*x - 136*x^2 + 55*x^3 + 190*x^4 + 645*x^5 - 626*x^6 + 953*x^7 - 409*x^8 - 178*x^9 + 30*x^10)). - Vaclav Kotesovec, Dec 09 2020