A121787 "Crossing walks hitting the center" on the square lattice (see Jensen web site for further information).

1, 10, 7056, 462755440, 2593165016903538, 1243982213040307428318660, 51166088445891978924432033203830714, 180349587397776823066172713933745722978533730900

Offset

0,2

Links

I. Jensen, Table of n, a(n) for n = 0..9 [from the Jensen link below; a(0)=1 prepended by Georg Fischer, Apr 03 2020]

I. Jensen, Series Expansions for Self-Avoiding Walks [Wayback Machine]

Formula

a(n) = A333685(n,n). - Seiichi Manyama, Apr 02 2020

Example

From Seiichi Manyama, Apr 01 2020: (Start)
a(1) = 10;
   S--*--*   S--*--*   S--*      S--*      S--*
         |         |      |         |         |
      +--*   *--+--*      +--*      +      *--+
      |      |               |      |      |
      *--E   *--*--E         E      *--E   *--*--E
   S  *--*   S  *--*   S         S         S
   |  |  |   |  |  |   |         |         |
   *  +  *   *--+  *   *  +--*   *--+--*   *--+
   |  |  |         |   |  |  |         |      |
   *--*  E         E   *--*  E         E      *--E
a(2) = 7056;
   S--*--*--*--*   S--*--*--*--*   S--*--*--*--*
               |               |               |
   *--*--*--*--*   *--*--*--*--*   *--*--*--*--*
   |               |               |
   *--*--+         *--*--+         *--*--+
         |               |               |
   *--*--*            *--*  *--*      *--*
   |                  |     |  |      |
   *--*--*--*--E      *--*--*  E      *--*--*--E
   ... and so on.
(End)

Prog

(Python)
# Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A121787(n):
    if n == 0: return 1
    universe = tl.grid(2 * n, 2 * n)
    GraphSet.set_universe(universe)
    start, goal = 1, (2 * n + 1) * (2 * n + 1)
    paths = GraphSet.paths(start, goal).including((start + goal) // 2)
    return paths.len()
print([A121787(n) for n in range(7)])  # Seiichi Manyama, Apr 01 2020

Crossrefs

Cf. A333674, A333685.

Sequence in context: A356041 A199520 A169621 * A304437 A358920 A108089

Adjacent sequences: A121784 A121785 A121786 * A121788 A121789 A121790

Keyword

nonn

Author

N. J. A. Sloane, Aug 30 2006

Extensions

a(0)=1 prepended by Seiichi Manyama, Apr 02 2020

Status

approved