A222200
Number of Hamiltonian cycles on n X n+1 square grid of points.
Original entry on oeis.org
1, 2, 14, 154, 5320, 301384, 49483138, 13916993782, 10754797724124, 14746957510647992, 53540340738182687296, 354282765498796010420944, 6040964455632840415885507728, 191678405883294971709423926242394, 15351055042300622367048024911122943712
Offset: 2
A333864
Number of Hamiltonian cycles on an n X 2*n grid.
Original entry on oeis.org
1, 4, 236, 18684, 32463802, 54756073582, 2365714170297014, 87106950271042689032, 88514516642574170326003422, 71598455565101470929617326988084, 1673219200189416324422979402201514800461, 29815394539834813572600735261571894552950941626, 15836807024750749574106724392556189684881848226515147589
Offset: 2
- 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.
-
# 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)])
a(10) and a(12) quoted from Olga's paper.
A213813
Number of Hamiltonian cycles in P_12 X P_n.
Original entry on oeis.org
0, 1, 32, 9770, 205832, 32463802, 966656134, 102283239429, 3913787773536, 328076475659033, 14746957510647992, 1076226888605605706, 53540340738182687296, 3593066312119675283778, 190433654636776931262392, 12142048779807437697982030, 669350612142203868221516908
Offset: 1
A360063
Triangle read by rows: T(m,n) is the number of Hamiltonian cycles in the graph whose nodes are the integer lattice points (x,y) with 0 <= x < m and 0 <= y < n, and with an edge between two nodes if there is no other integer lattice point on the line segment between them; 1 <= n <= m.
Original entry on oeis.org
0, 0, 3, 0, 24, 1152, 0, 354, 436416, 2595450592, 0, 8138, 129422880
Offset: 1
Triangle begins:
m\n| 1 2 3 4 5
---+-------------------------------
1 | 0
2 | 0 3
3 | 0 24 1152
4 | 0 354 436416 2595450592
5 | 0 8138 129422880 ? ?
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