A333864 - OEIS

%I #17 Apr 08 2020 17:45:14

%S 1,4,236,18684,32463802,54756073582,2365714170297014,

%T 87106950271042689032,88514516642574170326003422,

%U 71598455565101470929617326988084,1673219200189416324422979402201514800461,29815394539834813572600735261571894552950941626

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

%H 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 <a href="https://www.researchgate.net/publication/267115049_Enumeration_of_Hamiltonian_Cycles_in_Some_Grid_Graphs">Research Gate</a>.

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

%o (Python)

%o # Using graphillion

%o from graphillion import GraphSet

%o import graphillion.tutorial as tl

%o def A333864(n):

%o     universe = tl.grid(n - 1, 2 * n - 1)

%o     GraphSet.set_universe(universe)

%o     cycles = GraphSet.cycles(is_hamilton=True)

%o     return cycles.len()

%o print([A333864(n) for n in range(2, 8)])

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

%K nonn

%O 2,2

%A _Seiichi Manyama_, Apr 08 2020

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