A338963 Number of (undirected) paths in C_n X P_n.

1209, 103184, 21272810, 11481159930

Offset: 3

Author

Seiichi Manyama, Dec 18 2020

Keywords

• nonn
• more

Comments

a(8) = 70244258770074672.

Crossrefs

Cf. A268894, A338709, A338960, A338961, A338962.

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 A(start, goal, n, k):
    universe = make_CnXPk(n, k)
    GraphSet.set_universe(universe)
    paths = GraphSet.paths(start, goal)
    return paths.len()
def A338963(n):
    m = n * n
    s = 0
    for i in range(1, m):
        for j in range(i + 1, m + 1):
            s += A(i, j, n, n)
    return s
print([A338963(n) for n in range(3, 7)])