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%I #44 Feb 21 2020 11:10:24
%S 1,1,1,2,8,24,282,888,46933,238119,36027060,187011538,130162111969,
%T 1084873972934,2200211600730504,18559765767843341,
%U 174907641314142138422,2355130982684196593401,65250573687646264926302133,884112393542714503429381555
%N 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.
%C If you allow going down on the first step you get two times a(n) for n > 1.
%C 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.
%H S. Brunner, <a href="https://pastebin.com/9kxPM2hF">Python program</a>.
%H Peter Kagey, <a href="/A331001/a331001.pdf">Example of a(5) = 8</a>.
%e The solutions for n=3 and n=4:
%e n=3: | n=4:
%e 1 | 1 2
%e >>v | >>>v | >v>
%e v<< | v<<< | v<^<
%e >> | >>>v | v>v^
%e | <<< | >^>^
%Y Cf. A145157, A265914.
%K nonn,walk,hard,nice
%O 1,4
%A _S. Brunner_, Feb 02 2020
%E a(11)-a(20) from _Andrew Howroyd_, Feb 20 2020
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