A333323 Number of self-avoiding closed paths on an n X n grid which pass through NW and SE corners.

1, 3, 42, 1799, 232094, 92617031, 115156685746, 442641690778179, 5224287477491915786, 188825256606226776728029, 20879416139356164466643759334, 7057757437924198729598570424130207, 7287699030020917172151307665469211016474, 22973720258279267139936821063450448822110219653

Offset

2,2

Links

Anthony J. Guttmann and Iwan Jensen, Table of n, a(n) for n = 2..27

Anthony J. Guttmann and Iwan Jensen, Self-avoiding walks and polygons crossing a domain on the square and hexagonal lattices, arXiv:2208.06744 [math-ph], Aug 13 2022, Table D2 (with offset 1).

Anthony J. Guttmann and Iwan Jensen, The gerrymander sequence, or A348456, arXiv:2211.14482 [math.CO], 2022.

Example

a(2) = 1;
   +--*
   |  |
   *--+
a(3) = 3;
   +--*--*   +--*--*   +--*
   |     |   |     |   |  |
   *--*  *   *     *   *  *--*
      |  |   |     |   |     |
      *--+   *--*--+   *--*--+

Prog

(Python)
# Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A333323(n):
    universe = tl.grid(n - 1, n - 1)
    GraphSet.set_universe(universe)
    cycles = GraphSet.cycles().including(1).including(n * n)
    return cycles.len()
print([A333323(n) for n in range(2, 10)])

Crossrefs

Cf. A007764, A333246, A333247, A333466.

Cf. A121785, A356610-A356616, A354511.

Sequence in context: A268621 A218308 A195010 * A331705 A156108 A210929

Adjacent sequences: A333320 A333321 A333322 * A333324 A333325 A333326

Keyword

nonn

Author

Seiichi Manyama, Mar 23 2020

Extensions

a(11) from Seiichi Manyama, Apr 07 2020

a(10) and a(12)-a(15) from Vaclav Kotesovec, Aug 16 2022 (computed by Anthony Guttmann)

Status

approved