cp's OEIS Frontend

A333903 Number of directed Hamiltonian paths in a 2*n X n grid starting at the upper left corner and finishing in the lower left corner.

%I A333903 #29 Jun 29 2023 11:01:03
%S A333903 1,1,16,264,117852,43399371,443064195958,3575671586791915,
%T A333903 831655228913958996424,147303585340262824414389642,
%U A333903 774577888161337889995061257722609,3015734636186832309974653370241824509796,356606519352227259565296610082412177642016167446
%N A333903 Number of directed Hamiltonian paths in a 2*n X n grid starting at the upper left corner and finishing in the lower left corner.
%H A333903 Ed Wynn, <a href="/A333903/b333903.txt">Table of n, a(n) for n = 1..18</a>
%F A333903 a(n) = A271592(2*n,n).
%e A333903 a(1) = 1;
%e A333903    S
%e A333903    |
%e A333903    *
%e A333903    |
%e A333903    E
%e A333903 a(2) = 1;
%e A333903    S--*
%e A333903       |
%e A333903    *--*
%e A333903    |
%e A333903    *--*
%e A333903       |
%e A333903    E--*
%e A333903 a(3) = 16;
%e A333903    S--*--*   S--*--*   S--*--*   S--*--*
%e A333903          |         |         |         |
%e A333903    *--*--*   *--*--*   *--*--*   *--*--*
%e A333903    |         |         |         |
%e A333903    *--*--*   *--*--*   *  *--*   *  *--*
%e A333903          |         |   |  |  |   |  |  |
%e A333903    *--*--*   *--*  *   *--*  *   *  *  *
%e A333903    |         |  |  |         |   |  |  |
%e A333903    *--*--*   *  *  *   *--*  *   *--*  *
%e A333903          |   |  |  |   |  |  |         |
%e A333903    E--*--*   E  *--*   E  *--*   E--*--*
%e A333903    S--*--*   S--*--*   S--*--*   S--*--*
%e A333903          |         |         |         |
%e A333903    *--*  *   *--*  *   *--*  *   *--*  *
%e A333903    |  |  |   |  |  |   |  |  |   |  |  |
%e A333903    *  *--*   *  *--*   *  *  *   *  *  *
%e A333903    |         |         |  |  |   |  |  |
%e A333903    *--*--*   *  *--*   *  *--*   *  *  *
%e A333903          |   |  |  |   |         |  |  |
%e A333903    *--*  *   *--*  *   *--*--*   *  *  *
%e A333903    |  |  |         |         |   |  |  |
%e A333903    E  *--*   E--*--*   E--*--*   E  *--*
%e A333903    S  *--*   S  *--*   S  *--*   S  *--*
%e A333903    |  |  |   |  |  |   |  |  |   |  |  |
%e A333903    *--*  *   *--*  *   *--*  *   *--*  *
%e A333903          |         |         |         |
%e A333903    *--*--*   *--*--*   *--*  *   *--*  *
%e A333903    |         |         |  |  |   |  |  |
%e A333903    *--*--*   *  *--*   *  *--*   *  *  *
%e A333903          |   |  |  |   |         |  |  |
%e A333903    *--*  *   *--*  *   *--*--*   *  *  *
%e A333903    |  |  |         |         |   |  |  |
%e A333903    E  *--*   E--*--*   E--*--*   E  *--*
%e A333903    S  *--*   S  *--*   S  *--*   S  *--*
%e A333903    |  |  |   |  |  |   |  |  |   |  |  |
%e A333903    *  *  *   *  *  *   *  *  *   *  *  *
%e A333903    |  |  |   |  |  |   |  |  |   |  |  |
%e A333903    *--*  *   *--*  *   *  *  *   *  *  *
%e A333903          |         |   |  |  |   |  |  |
%e A333903    *--*--*   *--*  *   *--*  *   *  *  *
%e A333903    |         |  |  |         |   |  |  |
%e A333903    *--*--*   *  *  *   *--*  *   *--*  *
%e A333903          |   |  |  |   |  |  |         |
%e A333903    E--*--*   E  *--*   E  *--*   E--*--*
%o A333903 (Python)
%o A333903 # Using graphillion
%o A333903 from graphillion import GraphSet
%o A333903 import graphillion.tutorial as tl
%o A333903 def A333903(n):
%o A333903     universe = tl.grid(n - 1, 2 * n - 1)
%o A333903     GraphSet.set_universe(universe)
%o A333903     start, goal = 1, 2 * n
%o A333903     paths = GraphSet.paths(start, goal, is_hamilton=True)
%o A333903     return paths.len()
%o A333903 print([A333903(n) for n in range(1, 8)])
%Y A333903 Cf. A000532, A271592, A333604, A333606, A333863.
%K A333903 nonn
%O A333903 1,3
%A A333903 _Seiichi Manyama_, Apr 09 2020
%E A333903 a(9), a(11), a(13) from _Seiichi Manyama_
%E A333903 a(8), a(10), a(12), a(14)-a(18) from _Ed Wynn_, Jun 28 2023