A339142 Number of (undirected) cycles in the graph C_5 X P_n.

1, 52, 733, 9394, 119235, 1512196, 19177677, 243212478, 3084441599, 39117172360, 496087629441, 6291429718962, 79788500460003, 1011885230273244, 12832823194696645, 162747064808635206, 2063973507784856167, 26175505197898511728, 331960206747350288969, 4209950410912939269210

Offset: 1

Author

Seiichi Manyama, Nov 25 2020

Keywords

• nonn

Links

• Ed Wynn, Table of n, a(n) for n = 1..87
• Eric Weisstein's World of Mathematics, Graph Cycle

Crossrefs

Cf. A003731 (Hamiltonian cycles), A339117, A339136, A339137, A339140, 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 A339142(n):
    universe = make_CnXPk(5, n)
    GraphSet.set_universe(universe)
    cycles = GraphSet.cycles()
    return cycles.len()
print([A339142(n) for n in range(1, 9)])

Extensions

More terms from Ed Wynn, Jun 28 2023