A333583 Number of Hamiltonian paths in an 8 X (2n+1) grid starting at the lower left corner and finishing in the upper right corner.

1, 64, 6706, 851073, 114243216, 15695570146, 2178079125340, 303568139329711, 42388918310108440, 5923750747499881068, 828111786035239457647, 115782566867663040724929, 16189114623816733581826838, 2263672174616450290622937801, 316525123224847580237219904819

Offset: 0

Author

Seiichi Manyama, Mar 27 2020

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200
• Index entries for sequences related to graphs, Hamiltonian

Crossrefs

Cf. A014523, A333580.

Programs

Python

# Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A333580(n, k):
    if n == 1 or k == 1: return 1
    universe = tl.grid(n - 1, k - 1)
    GraphSet.set_universe(universe)
    start, goal = 1, k * n
    paths = GraphSet.paths(start, goal, is_hamilton=True)
    return paths.len()
def A333583(n):
    return A333580(8, 2 * n + 1)
print([A333583(n) for n in range(7)])

Extensions

Terms a(7) and beyond from Andrew Howroyd, Jan 30 2022