A333674 Number of self-avoiding closed paths on a (2*n+1) X (2*n+1) grid which pass through the center of (2*n+1) X (2*n+1) grid.

12, 6820, 377147460, 1839271833471556, 784401089017645862031632, 29302016786723196117858460309272916

Offset

1,1

Comments

a(n) is a multiple of 4.

Links

Table of n, a(n) for n=1..6.

Example

a(1) = 12;
   *--*--*   *--*--*   *--*--*   *--*      *--*      *--*
   |     |   |     |   |     |   |  |      |  |      |  |
   *--+  *   *  +--*   *--+--*   *  +--*   *  +      *--+
      |  |   |  |                |     |   |  |
      *--*   *--*                *--*--*   *--*
      *--*      *--*      *--*
      |  |      |  |      |  |
      +  *   *--+  *      +--*      +--*   *--+--*   *--+
      |  |   |     |                |  |   |     |   |  |
      *--*   *--*--*                *--*   *--*--*   *--*

Prog

(Python)
# Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A333674(n):
    universe = tl.grid(2 * n, 2 * n)
    GraphSet.set_universe(universe)
    cycles = GraphSet.cycles().including(2 * n * n + 2 * n + 1)
    return cycles.len()
print([A333674(n) for n in range(1, 6)])

Crossrefs

Cf. A121787.

Sequence in context: A208865 A012607 A167072 * A308130 A107251 A201493

Adjacent sequences: A333671 A333672 A333673 * A333675 A333676 A333677

Keyword

nonn,more,hard

Author

Seiichi Manyama, Apr 01 2020

Extensions

a(6) from Lucas A. Brown, Mar 19 2024

Status

approved