A339074 Number of (undirected) cycles in the graph C_3 X C_n.

312, 1531, 7298, 35205, 174268, 885719, 4601982, 24306577, 129851384, 698930787, 3780126106, 20505863069, 111441343860, 606312668335, 3300926292470, 17978225967081, 97939845566896, 533619551723963, 2907629293865874, 15844069824657013, 86338863686763692, 470492593924667271

Offset: 3

Author

Seiichi Manyama, Nov 22 2020

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 3..500
• Eric Weisstein's World of Mathematics, Graph Cycle
• Eric Weisstein's World of Mathematics, Torus Grid Graph

Crossrefs

Cf. A194952, A296527, A339075.

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 A339074(n):
    universe = make_CnXCk(n, 3)
    GraphSet.set_universe(universe)
    cycles = GraphSet.cycles()
    return cycles.len()
print([A339074(n) for n in range(3, 30)])