A333581 Number of Hamiltonian paths in a 6 X (2n+1) grid starting at the lower left corner and finishing in the upper right corner.

1, 16, 378, 10204, 286395, 8142184, 232408228, 6641558434, 189856823709, 5427696641303, 155171211771501, 4436158800822989, 126824318787312712, 3625748174071085779, 103655548766966797516, 2963380335725281547187, 84719269552230266413889, 2422015949371169505273833

Offset: 0

Author

Seiichi Manyama, Mar 27 2020

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..500
• 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 A333581(n):
    return A333580(6, 2 * n + 1)
print([A333581(n) for n in range(10)])

Extensions

Terms a(10) and beyond from Andrew Howroyd, Jan 30 2022