A333582 Number of Hamiltonian paths in a 7 X n grid starting at the lower left corner and finishing in the upper right corner.

1, 1, 32, 111, 1670, 10204, 111712, 851073, 8261289, 68939685, 637113287, 5521505724, 49977297839, 440051896440, 3947537767621, 34992551369200, 312684850861298, 2779712414621925, 24796726969942763, 220708765035288988, 1967401456946216789, 17520501580778152908

Offset

1,3

Links

Seiichi Manyama, Table of n, a(n) for n = 1..500

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 A333582(n):
    return A333580(n, 7)
print([A333582(n) for n in range(1, 25)])

Crossrefs

Row n=7 of A333580.

Cf. A014584.

Sequence in context: A337786 A233684 A218068 * A039464 A203728 A044283

Adjacent sequences: A333579 A333580 A333581 * A333583 A333584 A333585

Keyword

nonn

Author

Seiichi Manyama, Mar 27 2020

Status

approved