A333585 Number of Hamiltonian paths in a 10 X (2n+1) grid starting at the lower left corner and finishing in the upper right corner.

1, 256, 117204, 68939685, 43598351250, 28467653231928, 18879702000329222, 12620031290571348940, 8469937551020819909757, 5696439378813116535052879, 3835239247888770485464962184, 2583576672252172117218927779417, 1740899369113326621618848563838108

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 A333585(n):
    return A333580(10, 2 * n + 1)
print([A333585(n) for n in range(7)])

Extensions

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