This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A331001 #52 Jul 18 2025 14:48:36 %S A331001 1,1,1,2,8,24,282,888,46933,238119,36027060,187011538,130162111969, %T A331001 1084873972934,2200211600730504,18559765767843341, %U A331001 174907641314142138422,2355130982684196593401,65250573687646264926302133,884112393542714503429381555,114482128183138374886637093070429,2465467527044697154210112460659081 %N 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. %C A331001 If you allow going down on the first step you get two times a(n) for n > 1. %C A331001 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 A331001 S. Brunner, <a href="https://pastebin.com/9kxPM2hF">Python program</a>. %H A331001 Peter Kagey, <a href="/A331001/a331001.pdf">Example of a(5) = 8</a>. %e A331001 The solutions for n=3 and n=4: %e A331001 n=3: | n=4: %e A331001 1 | 1 2 %e A331001 >>v | >>>v | >v> %e A331001 v<< | v<<< | v<^< %e A331001 >> | >>>v | v>v^ %e A331001 | <<< | >^>^ %Y A331001 Cf. A145157, A265914. %K A331001 nonn,walk,hard,nice %O A331001 1,4 %A A331001 _S. Brunner_, Feb 02 2020 %E A331001 a(11)-a(20) from _Andrew Howroyd_, Feb 20 2020 %E A331001 a(21) from _Andrew Howroyd_, Oct 16 2024 %E A331001 a(22) from _Oliver R. Bellwood_, Jul 18 2025