A121785
"Spanning walks" on the square lattice (see Jensen web site for further information).
Original entry on oeis.org
8, 95, 2320, 154259, 30549774, 17777600753, 30283708455564, 152480475641255213, 2287842813828061810244, 102744826737618542833764649, 13848270995235582268846758977770
Offset: 1
A333323
Number of self-avoiding closed paths on an n X n grid which pass through NW and SE corners.
Original entry on oeis.org
1, 3, 42, 1799, 232094, 92617031, 115156685746, 442641690778179, 5224287477491915786, 188825256606226776728029, 20879416139356164466643759334, 7057757437924198729598570424130207, 7287699030020917172151307665469211016474, 22973720258279267139936821063450448822110219653
Offset: 2
a(2) = 1;
+--*
| |
*--+
a(3) = 3;
+--*--* +--*--* +--*
| | | | | |
*--* * * * * *--*
| | | | | |
*--+ *--*--+ *--*--+
- 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.
-
# 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)])
Showing 1-2 of 2 results.
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