A333584 Number of Hamiltonian paths in a 9 X n grid starting at the lower left corner and finishing in the upper right corner.

1, 1, 128, 624, 28417, 286395, 8261289, 114243216, 2688307514, 43598351250, 928370853748, 16331387665387, 330593938169845, 6062963019120077, 119575303856316650, 2240422461856052342, 43592076562463162280, 825830699757513748579, 15955080499901505066753

Offset: 1

Author

Seiichi Manyama, Mar 27 2020

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..200
• Index entries for sequences related to graphs, Hamiltonian

Crossrefs

Row n=9 of A333580.

Cf. A014584.

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 A333584(n):
    return A333580(n, 9)
print([A333584(n) for n in range(1, 20)])