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 A380813 #9 Jun 28 2025 11:05:13 %S A380813 0,0,-1,-2,-3,-3,-2,-1,1,2,3,3,2,1,0,-1,-1,0,2,3,4,5,5,4,2,0,-2,-4,-5, %T A380813 -6,-6,-5,-4,-2,0,2,4,5,6,6,6,5,3,1,-1,-3,-4,-4,-4,-3,-1,1,3,5,6,7,7, %U A380813 7,6,4,2,0,-2,-3,-4,-5,-5,-4,-3,-2,-1,0,1,1,0,-1 %N A380813 Sequence of y-coordinates of the lexicographically earliest (according to the spiral numbering of the square grid; see comments) infinite Racetrack trajectory (using von Neumann neighborhood) on the square grid. %C A380813 See A380812 for more details. %C A380813 See A351042 or Wikipedia link for a description of the rules of Racetrack. %C A380813 The trajectory in A351043 is defined in a similar way, but it does not backtrack when it gets stuck, so it is finite, ending after 146 steps. The trajectory here is identical to the trajectory in A351043 for the first 144 steps, and it turns out that the y-coordinates agree also for the last 2 steps. %H A380813 Pontus von Brömssen, <a href="/A380813/b380813.txt">Table of n, a(n) for n = 0..10000</a> %H A380813 Pontus von Brömssen, <a href="/A380812/a380812.png">Plot of the first 5000 steps of the trajectory</a>. %H A380813 Wikipedia, <a href="https://en.wikipedia.org/wiki/Racetrack_(game)">Racetrack</a>. %F A380813 a(n) = A274923(A351043(n)+1) for n <= 146. %Y A380813 Cf. A274923, A351042, A351043, A380812 (x-coordinates), A380814. %K A380813 sign %O A380813 0,4 %A A380813 _Pontus von Brömssen_, Feb 05 2025