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 A352388 #56 May 07 2022 09:56:03 %S A352388 0,0,0,0,5,21,127,618,2934,13542,61803,276650,1219508,5309179, %T A352388 22868295,97663066,414156142,1746438478 %N A352388 Number of solutions to Snake Number Problem for snakes with n-periodic instructions in an infinite square grid (see Comments). %C A352388 Given a list of n move instructions (up, right, down, left), the snake starts at the origin and moves according to the instructions, in order. If an instruction tells it to move to a square that has already been visited, the snake skips that instruction. After it has followed (or skipped) the last instruction in the list, it starts again with the first one. a(n) is the number of lists of n instructions that results in the snake getting stuck at some point. Lists of instructions that are equivalent under rotations and reflections are counted only once, so we can for example assume that the first instruction is "up", and that the first "right" comes before the first "left". But how does one know when to interrupt a snake and deem it infinite? - _Pontus von Brömssen_, May 05 2022 %C A352388 Computer solutions a(5) to a(13) found by Giorgio Vecchi. %C A352388 Computer solution a(14) to a(18) found by Ariel Futoransky. %H A352388 Ariel Futoransky, <a href="http://snake.puzzlefun.online/">Snake Program</a>, Snake Program to try the snakes, April 2022 (see bottom animation and label for different options). %H A352388 Rodolfo Kurchan, <a href="http://www.puzzlefun.online/problems">Puzzle Fun</a>, Snake Number Problem, March 2022. %e A352388 These are the 5 different solutions with 5 instructions: %e A352388 UURDL: 19 %e A352388 17 18 3 4 -- %e A352388 16 19 2 5 6 %e A352388 15 14 1 8 7 %e A352388 -- 13 10 9 -- %e A352388 -- 12 11 -- -- %e A352388 URDLL: 21 %e A352388 -- 19 20 -- -- -- %e A352388 17 18 21 2 3 -- %e A352388 16 15 14 1 4 5 %e A352388 -- 12 13 8 7 6 %e A352388 -- 11 10 9 -- -- %e A352388 URRDL: 24 %e A352388 -- -- 20 21 22 %e A352388 17 18 19 24 23 %e A352388 16 15 2 3 4 %e A352388 13 14 1 6 5 %e A352388 12 11 8 7 -- %e A352388 -- 10 9 -- -- %e A352388 URDLU: 26 %e A352388 -- -- 21 22 -- %e A352388 16 17 20 23 24 %e A352388 15 18 19 26 25 %e A352388 14 13 2 3 -- %e A352388 -- 12 1 4 5 %e A352388 -- 11 10 7 6 %e A352388 -- -- 9 8 -- %e A352388 URDDL: 30 %e A352388 -- -- 20 21 -- -- %e A352388 -- 18 19 22 23 -- %e A352388 16 17 2 3 24 -- %e A352388 15 14 1 4 25 26 %e A352388 12 13 6 5 30 27 %e A352388 11 10 7 -- 29 28 %e A352388 -- 9 8 -- -- -- %Y A352388 Cf. A353259, A353060, A353176, A004147. %K A352388 nonn,more %O A352388 1,5 %A A352388 _Rodolfo Kurchan_, Apr 29 2022