A333604 Number of directed Hamiltonian walks from NW to SW corners of an 8 X n grid.

1, 1, 64, 264, 6820, 52387, 909009, 8934966, 130373192, 1440623260, 19338414411, 226336038320, 2916455246831, 35119270968805, 443497762883269, 5416278334971240, 67721300861621626, 832844111255909543, 10362230473284966919

Offset: 1

Author

Seiichi Manyama, Mar 28 2020

Keywords

• nonn

Links

• Ed Wynn, Table of n, a(n) for n = 1..89

Crossrefs

Row n=8 of A271592.

Cf. A333583.

Programs

Python

# Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A271592(n, k):
    if k == 1: return 1
    universe = tl.grid(k - 1, n - 1)
    GraphSet.set_universe(universe)
    start, goal = 1, n
    paths = GraphSet.paths(start, goal, is_hamilton=True)
    return paths.len()
def A333604(n):
    return A271592(8, n)
print([A333604(n) for n in range(1, 9)])

Extensions

More terms from Ed Wynn, Jun 25 2023