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

1,3

Links

Seiichi Manyama, Table of n, a(n) for n = 1..200

Index entries for sequences related to graphs, Hamiltonian

Prog

(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)])

Crossrefs

Row n=9 of A333580.

Cf. A014584.

Sequence in context: A198072 A197906 A218903 * A349110 A366827 A297463

Adjacent sequences: A333581 A333582 A333583 * A333585 A333586 A333587

Keyword

nonn

Author

Seiichi Manyama, Mar 27 2020

Status

approved