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%I #34 Jul 30 2021 08:34:53
%S 0,0,1,0,-1,-1,0,1,2,1,0,-1,-2,-2,-1,0,1,2,3,2,1,0,-1,-2,-3,-3,-2,-1,
%T 0,1,2,3,4,3,2,1,0,-1,-2,-3,-4,-4,-3,-2,-1,0,1,2,3,4,5,4,3,2,1,0,-1,
%U -2,-3,-4,-5,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,5,4,3,2,1,0,-1,-2,-3
%N List of y-coordinates of a point moving in a smooth counterclockwise spiral rotated by Pi/4.
%H Hugo Pfoertner, <a href="/A305258/a305258.png">Illustration of spiral</a>.
%H <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>
%F a(n) = A053616(n)*sign(sin(Pi*(1+sqrt(1+8*n))/2)), so that abs(a(n)) = A053616(n).
%F a(n) = A010751(n-floor((1/2)*(sqrt(2n-1)+1))). - _William McCarty_, Jul 29 2021
%e Sequence gives y-coordinate of the n-th point of the following spiral:
%e d:
%e 4 | 32 49
%e | / \ \
%e 3 | 33 18 31 48
%e | / / \ \ \
%e 2 | 34 19 8 17 30 47
%e | / / / \ \ \ \
%e 1 | 35 20 9 2 7 16 29 46
%e | / / / / \ \ \ \ \
%e 0 | 36 21 10 3 0---1 6 15 28 45
%e | \ \ \ \ / / / /
%e -1 | 37 22 11 4---5 14 27 44
%e | \ \ \ / / /
%e -2 | 38 23 12--13 26 43
%e | \ \ / /
%e -3 | 39 24--25 42
%e | \ /
%e -4 | 40--41
%e _______________________________________
%e x: -4 -3 -2 -1 0 1 2 3 4 5
%o (PARI) up=-1;print1(x=0,", ");for(stride=1,12,up=-up;x+=stride;y=x+stride+1;for(k=x,y-1,print1(up*min(k-x,y-k), ", "))) \\ _Hugo Pfoertner_, Jun 02 2018
%Y A010751 gives sequence of x-coordinates.
%Y Cf. A053616.
%Y Cf. A000384, A001105, A002024, A014105, A046092.
%K sign
%O 0,9
%A _Hugo Pfoertner_, May 29 2018
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