A333864 - OEIS

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A333864

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

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,2

LINKS

Table of n, a(n) for n=2..13.

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.

FORMULA

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

PROG

(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()