A338960 Number of (undirected) paths in C_4 X P_n.

12, 444, 7584, 103184, 1246892, 14010212, 150042016, 1554630384, 15735477148, 156604841764, 1539509238384, 14997746124304, 145132198165132, 1397493793301476, 13407313676392384, 128278229316758192, 1224872135665718780, 11678406201771406628, 111224649402691424912, 1058446545979095492816

Offset: 1

Author

Seiichi Manyama, Dec 18 2020

Keywords

• nonn

Links

• Table of n, a(n) for n = 1..20

Crossrefs

Cf. A003752, A338709, A338961, A338962, A338963.

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 B(n, k):
    m = k * n
    s = 0
    for i in range(1, m):
        for j in range(i + 1, m + 1):
            s += A(i, j, n, k)
    return s
def A338960(n):
    return B(4, n)
print([A338960(n) for n in range(1, 11)])