A339075 Number of (undirected) cycles in the graph C_4 X C_n.

1531, 14704, 132089, 1165194, 10254423, 90693764, 808627861, 7276584222, 66085185907, 605303076120, 5585690299505, 51868931553714, 484136128508431, 4537416076416428, 42662439747995981, 402124615161547590, 3797500862839734443, 35913373920441057600, 340000796575687888937

Offset: 3

Author

Seiichi Manyama, Nov 22 2020

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 3..100
• Eric Weisstein's World of Mathematics, Graph Cycle
• Eric Weisstein's World of Mathematics, Torus Grid Graph

Crossrefs

Cf. A216588, A296527, A339074.

Programs

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 A339075(n):
    universe = make_CnXCk(4, n)
    GraphSet.set_universe(universe)
    cycles = GraphSet.cycles()
    return cycles.len()
print([A339075(n) for n in range(3, 30)])