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A174344 List of x-coordinates of point moving in clockwise spiral. 1
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)
OFFSET

1,10

REFERENCES

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

LINKS

Table of n, a(n) for n=1..31.

S. Mustonen, Ulam spiral in color [From Seppo Mustonen, Aug 21 2010]

FORMULA

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)

EXAMPLE

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

...........

MATHEMATICA

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]

CROSSREFS

Cf. A180714.

Sequence in context: A159782 A216953 A124752 * A049241 A230415 A101080

Adjacent sequences:  A174341 A174342 A174343 * A174345 A174346 A174347

KEYWORD

sign

AUTHOR

Nikolas Garofil (nikolas(AT)garofil.be), Mar 16 2010

EXTENSIONS

Link corrected by Seppo Mustonen, Sep 05 2010

Clarified definition - N. J. A. Sloane, Dec 20 2012

STATUS

approved

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Last modified November 23 09:53 EST 2014. Contains 249840 sequences.