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 A353176 #64 May 09 2022 15:17:04 %S A353176 30,79,152,450,241,257,1098,1448,9520,8804,8338,11348,25316,18823 %N A353176 Maximum length of a finite snake in the Snake Number Problem with n-periodic instructions in an infinite square grid (see Comments). %C A353176 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. The snake is either finite (if it gets stuck at some point) or infinite (if it can go on forever). a(n) is the maximum number of squares visited by a finite snake. For n <= 4, all snakes are infinite. - _Pontus von Brömssen_, May 08 2022 %H A353176 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 A353176 Rodolfo Kurchan, <a href="http://www.puzzlefun.online/problems">Puzzle Fun</a>, Snake Number Problem, March 2022. %e A353176 a(5) = 30 %e A353176 URDDL: 30 %e A353176 -- -- 20 21 -- -- %e A353176 -- 18 19 22 23 -- %e A353176 16 17 02 03 24 -- %e A353176 15 14 01 04 25 26 %e A353176 12 13 06 05 30 27 %e A353176 11 10 07 -- 29 28 %e A353176 -- 09 08 -- -- -- %e A353176 . %e A353176 a(6) = 79 %e A353176 UURDLL: 79 %e A353176 -- -- -- -- -- -- -- 74 75 -- -- %e A353176 -- -- -- -- -- 69 70 73 76 77 -- %e A353176 -- -- -- 64 65 68 71 72 79 78 -- %e A353176 -- -- -- 63 66 67 -- 27 28 -- -- %e A353176 -- -- 61 62 -- 22 23 26 29 30 -- %e A353176 56 57 60 17 18 21 24 25 32 31 -- %e A353176 55 58 59 16 19 20 03 04 33 34 -- %e A353176 54 53 52 15 14 13 02 05 06 35 36 %e A353176 -- -- 51 -- -- 12 01 08 07 38 37 %e A353176 -- -- 50 49 48 11 10 09 40 39 -- %e A353176 -- -- -- -- 47 -- 43 42 41 -- -- %e A353176 -- -- -- -- 46 45 44 -- -- -- -- %e A353176 . %e A353176 n | Number of finite solutions | Maximum length | Instructions that give %e A353176 | A352388(n) | a(n) | the maximum length %e A353176 ------------------------------------------------------------------------- %e A353176 5 5 30 URDDL %e A353176 6 21 79 UURDLL %e A353176 7 127 152 URULLDD %e A353176 8 618 450 URURUULD %e A353176 9 2934 241 URRRRDLRR %e A353176 10 13542 257 URRLDLRRUR %e A353176 11 61803 1098 URUURUUULLD %e A353176 12 276650 1448 URUULLDUDDDD %e A353176 13 1219508 9520 URRRLLDLRRULL %e A353176 14 5309179 8804 URRURRRLDLRULL %e A353176 15 22868295 8338 UDDRULUUUULLULD %e A353176 16 97663066 11348 URRURRRLDDLRUULL %e A353176 17 414156142 25316 URRRDLULUUUUULURL %e A353176 18 1746438478 18823 UDDDRULULLULLUULDU %e A353176 Computer solutions a(5) to a(13) found by Giorgio Vecchi. %e A353176 Computer solutions a(14) to a(18) found by Ariel Futoransky. %Y A353176 Cf. A352388, A353259, A353060, A028444. %K A353176 nonn,more %O A353176 5,1 %A A353176 _Rodolfo Kurchan_, Apr 28 2022