A333863 Number of Hamiltonian paths in a 2*(2*n+1) X (2*n+1) grid starting at the upper left corner and finishing in the lower right corner.

1, 16, 117204, 440051896440, 825830699757513748579, 769203260676279544212492116449800, 354179806054404909542325896762875458037457353029, 80433401895946253522491939742836167238530417144721958187080077425

Offset: 0

Author

Seiichi Manyama, Apr 08 2020

Keywords

• nonn

Links

• Ed Wynn, Table of n, a(n) for n = 0..9

Crossrefs

Cf. A001184, A333580, A333585, A333864.

Programs

Python

# Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A333863(n):
    universe = tl.grid(4 * n + 1, 2 * n)
    GraphSet.set_universe(universe)
    start, goal = 1, 2 * (2 * n + 1) ** 2
    paths = GraphSet.paths(start, goal, is_hamilton=True)
    return paths.len()
print([A333863(n) for n in range(7)])

Formula

a(n) = A333580(2*(2*n+1), 2*n+1).

Extensions

More terms from Ed Wynn, Jun 28 2023