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A305258
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List of y-coordinates of a point moving in a smooth counterclockwise spiral rotated by Pi/4.
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6
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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, 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, -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
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OFFSET
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0,9
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LINKS
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FORMULA
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a(n) = A053616(n)*sign(sin(Pi*(1+sqrt(1+8*n))/2)), so that abs(a(n)) = A053616(n).
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EXAMPLE
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Sequence gives y-coordinate of the n-th point of the following spiral:
d:
4 | 32 49
| / \ \
3 | 33 18 31 48
| / / \ \ \
2 | 34 19 8 17 30 47
| / / / \ \ \ \
1 | 35 20 9 2 7 16 29 46
| / / / / \ \ \ \ \
0 | 36 21 10 3 0---1 6 15 28 45
| \ \ \ \ / / / /
-1 | 37 22 11 4---5 14 27 44
| \ \ \ / / /
-2 | 38 23 12--13 26 43
| \ \ / /
-3 | 39 24--25 42
| \ /
-4 | 40--41
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x: -4 -3 -2 -1 0 1 2 3 4 5
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PROG
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(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
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CROSSREFS
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A010751 gives sequence of x-coordinates.
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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