A333689 Number of self-avoiding paths in (2*n+1) X 5 grid starting the upper left corner, passing through the center of grid and finishing the lower right corner.

1, 101, 7056, 610765, 53968755, 4775133828, 422813081886, 37441305792927, 3315577406171322, 293609559097456363, 26000534802119070508, 2302473191851860468948, 203895143590466986654399, 18055900558029962460378646, 1598937211532791928425001493, 141593611215040047912334138664

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..500

Prog

(Python)
# Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A333685(n, k):
    if n == 0 or k == 0: return 1
    universe = tl.grid(2 * n, 2 * k)
    GraphSet.set_universe(universe)
    start, goal = 1, (2 * n + 1) * (2 * k + 1)
    paths = GraphSet.paths(start, goal).including((start + goal) // 2)
    return paths.len()
def A333689(n):
    return A333685(n, 2)
print([A333689(n) for n in range(15)])

Crossrefs

Column 2 of A333685.

Sequence in context: A167626 A017764 A217677 * A291990 A303572 A152756

Adjacent sequences: A333686 A333687 A333688 * A333690 A333691 A333692

Keyword

nonn

Author

Seiichi Manyama, Apr 02 2020

Status

approved