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A331001
Number of symmetrical self-avoiding walks with maximum length on an n X n board which start in the upper left corner and go right on the first step.
2
1, 1, 1, 2, 8, 24, 282, 888, 46933, 238119, 36027060, 187011538, 130162111969, 1084873972934, 2200211600730504, 18559765767843341, 174907641314142138422, 2355130982684196593401, 65250573687646264926302133, 884112393542714503429381555, 114482128183138374886637093070429
OFFSET
1,4
COMMENTS
If you allow going down on the first step you get two times a(n) for n > 1.
All symmetrical self-avoiding walks on a square board with odd length seem to have a 180-degree rotational symmetry, and all symmetrical self-avoiding walks on a square board with even length seem to have either vertically or horizontally reflection symmetry.
EXAMPLE
The solutions for n=3 and n=4:
n=3: | n=4:
1 | 1 2
>>v | >>>v | >v>
v<< | v<<< | v<^<
>> | >>>v | v>v^
| <<< | >^>^
CROSSREFS
Sequence in context: A071599 A047695 A093842 * A050971 A118855 A009515
KEYWORD
nonn,walk,hard,nice
AUTHOR
S. Brunner, Feb 02 2020
EXTENSIONS
a(11)-a(20) from Andrew Howroyd, Feb 20 2020
a(21) from Andrew Howroyd, Oct 16 2024
STATUS
approved