%I #47 Apr 01 2023 11:22:24
%S 0,1,2,1,4,5,2,5,4,1,2,1,4,5,2,5,4,9,10,5,8,5,10,9,16,17,10,13,8,13,
%T 10,17,16,9,10,5,8,5,10,9,16,17,10,13,8,13,10,17,16,25,26,17,20,13,18,
%U 13,20,17,26,25,36,37,26,29,20,25,18,25,20,29,26,37,36,25,26,17,20,13,18,13,20
%N a(n) = squared distance to the origin of the n-th vertex on a counterclockwise undulating spiral in a square grid.
%C The spiral coordinates are A359216 and A359217.
%H Rémy Sigrist, <a href="/A359058/b359058.txt">Table of n, a(n) for n = 0..10081</a>
%H Hans G. Oberlack, <a href="/A359058/a359058_1.pdf">Undulating counterclockwise spiral in a square grid</a>
%H Rémy Sigrist, <a href="/A359058/a359058.gp.txt">PARI program</a>
%F a(n) = A359216(n)^2 + A359217(n)^2.
%e The spiral begins as follows and for instance point n=7 is at x=-2,y=1 so that a(7) = (-2)^2 + 1^2 = 5.
%e y ^
%e |
%e 4 | 17--16
%e | | |
%e 3 | 13--10 9--10
%e | | |
%e 2 | 13---8 5---4 5---8
%e | | | | |
%e 1 | 17--10 5---2 1---2 5--10
%e | | | | |
%e 0 | 16---9 4---1 0---1 4---9
%e | | | | |
%e -1 | 10---5 2---1 2---5 10--17
%e | | | | |
%e -2 | 8---5 4---5 8--13
%e | | |
%e -3 | 10---9 10--13
%e | | |
%e -4 | 16--17
%e +------------------------------------>
%e -4 -3 -2 -1 0 1 2 3 4 x
%o (PARI) See Links section.
%Y Cf. A001481, A336336, A359216, A359217.
%K nonn,easy
%O 0,3
%A _Hans G. Oberlack_, Dec 14 2022