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 A180714 #20 Aug 17 2018 19:42:23 %S A180714 0,1,2,1,0,-1,-2,-1,0,1,2,3,4,3,2,1,0,-1,-2,-3,-4,-3,-2,-1,0,1,2,3,4, %T A180714 5,6,5,4,3,2,1,0,-1,-2,-3,-4,-5,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,7, %U A180714 6,5,4,3,2,1,0,-1,-2,-3,-4,-5,-6,-7,-8,-7,-6,-5,-4,-3,-2,-1,0,1 %N A180714 Sum of the x- and y-coordinates of a point moving in a clockwise spiral. %C A180714 A spiral on the simple square grid is constructed starting at (0,0) and walking in the closest self-avoiding clockwise loop: up 1 unit, right 1 unit, down 2 units, left 2 units, up 3 units etc. The step widths in the x-coordinate are 0, 1, 0, -2, 0, 3, ... a signed version of A142150; the step widths in the y-coordinate are 1, 0, -2, 0, 3, ... The x-coordinate after n steps (n>=0) is a signed variant of A002265(n+3), namely 0, 0, 1, 1, -1, -1, 2, 2, -2, -2, 3, ...; the y-coordinate after n steps is 0, 1, 1, -1, -1, 2, 2, ... (n >= 0). The sum of the x- and y-coordinates after n steps (at corners of the spiral) is c(n) = 0, 1, 2, 0, -2, 1, 4, 0, -4, 1, 6, 0, -6, 1, 8, 0, ..., with g.f. -x*(1+x)/( (x-1)*(x^2+1)^2). The current sequence is obtained by recording the sum of the two coordinates at all intermediate positions walking with a stride of 1 along the edges of the spiral, equivalent to showing all interpolating integers between two values of c(n). The first differences a(n+1)-a(n) are two 1's, four -1's, six 1's, eight -1's etc., blocks of +1 and -1 with run lengths increasing by 2. - _R. J. Mathar_, Jan 22 2011 %H A180714 Peter Kagey, <a href="/A180714/b180714.txt">Table of n, a(n) for n = 0..10000</a> %H A180714 <a href="http://web.archive.org/web/20080306030905/http://et.bgcbellevue.org/logo/basic-loops.html">Image of the spiral</a> %e A180714 Spiral begins at x=0, y=0, then moves up-right-down-left-up-right-... %e A180714 a(0)=0+0=0, a(1)=1+0=1, a(2)=1+1=2, a(3)=0+1=1, a(4)=-1+1=0, a(5)=-1+0=-1, ... %Y A180714 Cf. A065358, A174344. %K A180714 sign %O A180714 0,3 %A A180714 _Vladimir Joseph Stephan Orlovsky_, Jan 21 2011