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A174344
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List of x-coordinates of point moving in clockwise spiral.
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1
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0, 1, 1, 0, -1, -1, -1, 0, 1, 2, 2, 2, 2, 1, 0, -1, -2, -2, -2, -2, -2, -1, 0, 1, 2, 3, 3, 3, 3, 3, 3
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,10
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REFERENCES
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Aaron Snook, Augmented Integer Linear Recurrences, http://www.cs.cmu.edu/afs/cs/user/mjs/ftp/thesis-program/2012/theses/snook.pdf, 2012. - From N. J. A. Sloane, Dec 19 2012
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LINKS
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Table of n, a(n) for n=1..31.
S. Mustonen, Ulam spiral in color [From Seppo Mustonen, Aug 21 2010]
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FORMULA
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Contribution from Seppo Mustonen, Aug 21 2010: (Start)
a(n)=a(n-1)+sin(mod(floor(sqrt(4*(n-1)+1)),4)*Pi/2)
For a corresponding formula for the Y coordinate, replace sin by -cos. (End)
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EXAMPLE
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Here is the beginning of the spiral. Sequence gives x-coordinate of the n-th point.
....
. 20 21 22 23 24 25
. 19 .6 .7 .8 .9 26
. 18 .5 .0 .1 10 27
. 17 .4 .3 .2 11 28
. 16 15 14 13 12 29
. 35 34 33 32 32 30
...........
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MATHEMATICA
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a[n_]:=a[n]=If[n==0, 0, a[n-1]+Sin[Mod[Floor[Sqrt[4*(n-1)+1]], 4]*Pi/2]]; Table[a[n], {n, 0, 50}] [From Seppo Mustonen, Aug 21 2010]
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CROSSREFS
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Cf. A180714.
Sequence in context: A159782 A216953 A124752 * A049241 A101080 A130836
Adjacent sequences: A174341 A174342 A174343 * A174345 A174346 A174347
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KEYWORD
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sign
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AUTHOR
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Nikolas Garofil (nikolas(AT)garofil.be), Mar 16 2010
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EXTENSIONS
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Link corrected by Seppo Mustonen, Sep 05 2010
Clarified definition - N. J. A. Sloane, Dec 20 2012
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STATUS
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approved
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