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 A329972 #30 Sep 19 2020 02:53:10
%S A329972 0,0,1,0,-1,-1,-1,-1,-1,-1,0,1,2,1,0,-1,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,
%T A329972 -1,0,1,2,3,2,1,0,-1,-2,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-2,
%U A329972 -1,0,1,2,3,4,3,2,1,0,-1,-2,-3,-4
%N A329972 Y-coordinate of a point moving in a triangular spiral.
%C A329972 A329116 gives x-coordinates for a point moving in counterclockwise triangular spiral.
%H A329972 Rémy Sigrist, <a href="/A329972/b329972.txt">Table of n, a(n) for n = 0..10000</a>
%H A329972 <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>
%F A329972 a(n) = floor(min(s*max(((0, 2*s) mod 2) - 2), (-2*s*s) mod (-1)) + ceiling(-s/2)) where s=sqrt(n).
%e A329972 y
%e A329972 |
%e A329972 4 | 56
%e A329972 | \
%e A329972 | \
%e A329972 | \
%e A329972 3 | 30 55
%e A329972 | / \ \
%e A329972 | / \ \
%e A329972 | / \ \
%e A329972 2 | 31 12 29 54
%e A329972 | / / \ \ \
%e A329972 | / / \ \ \
%e A329972 | / / \ \ \
%e A329972 1 | 32 13 2 11 28 53
%e A329972 | / / / \ \ \ \
%e A329972 | / / / \ \ \ \
%e A329972 | / / / \ \ \ \
%e A329972 0 | 33 14 3 0---1 10 27 52
%e A329972 | / / / \ \ \
%e A329972 | / / / \ \ \
%e A329972 | / / / \ \ \
%e A329972 -1 | 34 15 4---5---6---7---8---9 26 51
%e A329972 | / / \ \
%e A329972 | / / \ \
%e A329972 | / / \ \
%e A329972 -2 | 35 16--17--18--19--20--21--22--23--24--25 50
%e A329972 | / \
%e A329972 | / \
%e A329972 | / \
%e A329972 -3 | 36--37--38--39--40--41--42--43--44--45--46--47--48--49
%e A329972 |
%e A329972 +--------------------------------------------------------
%e A329972 x: -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
%t A329972 a[n_] := Table[Floor[Min[#*Max[0, 2*Mod[#, 2] - 2], -2*#*Mod[#, -1]] + Ceiling[-#/2]] &[Sqrt@ k], {k, 0, n}]; a[64]
%Y A329972 Cf. A268038, A274923.
%K A329972 sign,look
%O A329972 0,13
%A A329972 _Mikk Heidemaa_, Nov 26 2019