A333583 Number of Hamiltonian paths in an 8 X (2n+1) grid starting at the lower left corner and finishing in the upper right corner.

1, 64, 6706, 851073, 114243216, 15695570146, 2178079125340, 303568139329711, 42388918310108440, 5923750747499881068, 828111786035239457647, 115782566867663040724929, 16189114623816733581826838, 2263672174616450290622937801, 316525123224847580237219904819

Offset

0,2

Links

Andrew Howroyd, Table of n, a(n) for n = 0..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 A333583(n):
    return A333580(8, 2 * n + 1)
print([A333583(n) for n in range(7)])

Crossrefs

Cf. A014523, A333580.

Sequence in context: A085525 A349506 A264188 * A183243 A264075 A223198

Adjacent sequences: A333580 A333581 A333582 * A333584 A333585 A333586

Keyword

nonn

Author

Seiichi Manyama, Mar 27 2020

Extensions

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

Status

approved