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 A307012 #24 Jul 25 2021 02:16:25 %S A307012 0,0,1,1,0,-1,-1,-1,0,1,2,2,2,1,0,-1,-2,-2,-2,-2,-1,0,1,2,3,3,3,3,2,1, %T A307012 0,-1,-2,-3,-3,-3,-3,-3,-2,-1,0,1,2,3,4,4,4,4,4,3,2,1,0,-1,-2,-3,-4, %U A307012 -4,-4,-4,-4,-4,-3,-2,-1,0,1,2,3,4,5,5,5,5,5,5,4 %N A307012 Second coordinate in a redundant hexagonal coordinate system of the points of a counterclockwise spiral on an hexagonal grid. First and third coordinates are given in A307011 and A345978. %C A307012 The coordinate system can be described using 3 axes that pass through spiral point 0 and one of points 1, 2 or 3. Along each axis, one of the coordinates is 0. a(n) is the signed distance from spiral point n to the axis that passes through point 1. The distance is measured along either of the lines through point n that are parallel to one of the other 2 axes and the sign is such that point 2 has positive distance. - _Peter Munn_, Jul 13 2021 %C A307012 We can use this coordinate with the first coordinate to form an oblique coordinate system, in which each coordinate maps to an oblique coordinate vector parallel to the axis along which the other coordinate is 0. See the figure with nonperpendicular axes in the Barile link. When both of these coordinates are positive, the oblique coordinate vectors make a 60-degree angle with each other. [Made more specific by _Peter Munn_, Jul 19 2021] %H A307012 Hugo Pfoertner, <a href="/A307012/b307012.txt">Table of n, a(n) for n = 0..10150</a> %H A307012 Margherita Barile, <a href="https://mathworld.wolfram.com/ObliqueCoordinates.html">Oblique Coordinates</a>, entry in Eric Weisstein's World of Mathematics. %H A307012 HandWiki, <a href="https://handwiki.org/wiki/Hexagonal_lattice">Hexagonal Lattice</a>. %H A307012 Peter Munn, <a href="/A307012/a307012.png">Illustration of signed distance of spiral points</a>. %H A307012 Wikipedia, <a href="https://en.m.wikipedia.org/wiki/Signed_distance_function">Signed distance function</a>. %H A307012 <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a> %Y A307012 Cf. A307011, A307013, A328818, A334493, A345435, A345978. %K A307012 sign,look %O A307012 0,11 %A A307012 _Hugo Pfoertner_, Mar 19 2019 %E A307012 Name revised by _Peter Munn_, Jul 08 2021