A333864 Number of Hamiltonian cycles on an n X 2*n grid.

1, 4, 236, 18684, 32463802, 54756073582, 2365714170297014, 87106950271042689032, 88514516642574170326003422, 71598455565101470929617326988084, 1673219200189416324422979402201514800461, 29815394539834813572600735261571894552950941626, 15836807024750749574106724392556189684881848226515147589

Offset: 2

Author

Seiichi Manyama, Apr 08 2020

Keywords

• nonn

Links

• Huaide Cheng, Table of n, a(n) for n = 2..16
• Olga Bodroža-Pantić, B. Pantić, I. Pantić AND M. Bodroža-Solarov: Enumeration of Hamiltonian cycles in some grid grafs. MATCH Commun. Math. Comput. Chem. 70:1 (2013), 181-204. on Research Gate.

Crossrefs

Cf. A003763, A005390, A145416, A160149, A180505, A321172, A333863.

Programs

Python

# Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A333864(n):
    universe = tl.grid(n - 1, 2 * n - 1)
    GraphSet.set_universe(universe)
    cycles = GraphSet.cycles(is_hamilton=True)
    return cycles.len()
print([A333864(n) for n in range(2, 8)])

Formula

a(n) = A321172(n,2*n).

Extensions

a(10) and a(12) quoted from Olga's paper.

a(14) from Huaide Cheng, Jul 02 2025