A333438 Number of self-avoiding walks of any length from NW corner to its adjacent points on an n X n grid or lattice.

4, 16, 196, 8224, 1064540, 424745876, 527417814424, 2026136052712752, 23910840138416191440, 864203211903812503254788, 95556814333495667660116008300, 32299777937527326896385272155961508, 33351573725052992639783414388307775101504, 105136332761744656894957880833209728891149151420

Offset: 2

Author

Seiichi Manyama, Mar 21 2020

Keywords

• nonn

Examples

			a(2) = 4;
   S--E   S  E
          |  |
          *--*
   S      S--*
   |         |
   E      E--*
a(3) = 16;
   S--E      S  E      S  E--*   S  E--*
             |  |      |     |   |     |
             *--*      *--*--*   *     *
                                 |     |
                                 *--*--*
   S  E      S  E--*   S  E--*   S  E
   |  |      |     |   |     |   |  |
   *  *      *  *--*   *--*  *   *  *--*
   |  |      |  |         |  |   |     |
   *--*      *--*         *--*   *--*--*
   S         S--*      S--*      S--*--*
   |            |         |            |
   E         E--*      E  *      E     *
                       |  |      |     |
                       *--*      *--*--*
   S--*--*   S--*--*   S--*      S--*--*
         |         |      |            |
   E--*--*   E  *--*   E  *--*   E--*  *
             |  |      |     |      |  |
             *--*      *--*--*      *--*
		

Links

• Ed Wynn, Table of n, a(n) for n = 2..19

Crossrefs

Cf. A271507, A333439.

Programs

Python

# Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A333438(n):
    universe = tl.grid(n - 1, n - 1)
    GraphSet.set_universe(universe)
    start, goal = 1, 2
    paths = GraphSet.paths(start, goal)
    return paths.len() * 2
print([A333438(n) for n in range(2, 10)])

Extensions

a(11) and a(13) from Seiichi Manyama

More terms from Ed Wynn, Jun 29 2023