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 A343203 #11 May 27 2021 11:14:39 %S A343203 0,1,1,-1,-3,-2,-1,0,1,2,2,2,2,0,-2,-4,-6,-5,-4,-3,-2,-1,0,1,2,3,3,3, %T A343203 3,3,3,1,-1,-3,-5,-7,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,4,4,4,4,4,4, %U A343203 4,2,0,-2,-4,-6,-8,-10,-12,-11,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,5,5,5,5,5,5,5,5,5,3,1,-1,-3,-5,-7,-9,-11,-13,-15 %N A343203 Sum of x- and y-coordinate of a point moving in a triangular spiral. %e A343203 y %e A343203 | %e A343203 4 | 56 %e A343203 | \ %e A343203 | \ %e A343203 | \ %e A343203 3 | 30 55 %e A343203 | / \ \ %e A343203 | / \ \ %e A343203 | / \ \ %e A343203 2 | 31 12 29 54 %e A343203 | / / \ \ \ %e A343203 | / / \ \ \ %e A343203 | / / \ \ \ %e A343203 1 | 32 13 2 11 28 53 %e A343203 | / / / \ \ \ \ %e A343203 | / / / \ \ \ \ %e A343203 | / / / \ \ \ \ %e A343203 0 | 33 14 3 0---1 10 27 52 %e A343203 | / / / \ \ \ %e A343203 | / / / \ \ \ %e A343203 | / / / \ \ \ %e A343203 -1 | 34 15 4---5---6---7---8---9 26 51 %e A343203 | / / \ \ %e A343203 | / / \ \ %e A343203 | / / \ \ %e A343203 -2 | 35 16--17--18--19--20--21--22--23--24--25 50 %e A343203 | / \ %e A343203 | / \ %e A343203 | / \ %e A343203 -3 | 36--37--38--39--40--41--42--43--44--45--46--47--48--49 %e A343203 | %e A343203 +-------------------------------------------------------- %e A343203 x: -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 %e A343203 Count as follows. Start at n=0 with coordinates (0,0). So first term is 0. %e A343203 Next step is to move to n=1 with coordinates (1,0) resulting in sum=1. So the sequence begins 0,1,... %e A343203 Next step is to move to n=2 with coordinates (0,1) resulting in sum=1. So the sequence begins 0,1,1,... %e A343203 Next step is to move to n=3 with coordinates (-1,0) resulting in sum=-1. So the sequence begins 0,1,1,1,... %e A343203 Next step is to move to n=4 with coordinates (-2,-1) resulting in sum=-3. So the sequence begins 0,1,1,-1,-3,... %e A343203 and so on. %Y A343203 Cf. A329972, A329116. %K A343203 sign %O A343203 0,5 %A A343203 _Hans G. Oberlack_, Apr 07 2021