This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A333864 #30 Jul 02 2025 09:50:34 %S A333864 1,4,236,18684,32463802,54756073582,2365714170297014, %T A333864 87106950271042689032,88514516642574170326003422, %U A333864 71598455565101470929617326988084,1673219200189416324422979402201514800461,29815394539834813572600735261571894552950941626,15836807024750749574106724392556189684881848226515147589 %N A333864 Number of Hamiltonian cycles on an n X 2*n grid. %H A333864 Huaide Cheng, <a href="/A333864/b333864.txt">Table of n, a(n) for n = 2..16</a> %H A333864 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 A333864 a(n) = A321172(n,2*n). %o A333864 (Python) %o A333864 # Using graphillion %o A333864 from graphillion import GraphSet %o A333864 import graphillion.tutorial as tl %o A333864 def A333864(n): %o A333864 universe = tl.grid(n - 1, 2 * n - 1) %o A333864 GraphSet.set_universe(universe) %o A333864 cycles = GraphSet.cycles(is_hamilton=True) %o A333864 return cycles.len() %o A333864 print([A333864(n) for n in range(2, 8)]) %Y A333864 Cf. A003763, A005390, A145416, A160149, A180505, A321172, A333863. %K A333864 nonn %O A333864 2,2 %A A333864 _Seiichi Manyama_, Apr 08 2020 %E A333864 a(10) and a(12) quoted from Olga's paper. %E A333864 a(14) from _Huaide Cheng_, Jul 02 2025