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A333323
Number of self-avoiding closed paths on an n X n grid which pass through NW and SE corners.
6
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)])
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