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A329972 Y-coordinate of a point moving in a triangular spiral. 4
0, 0, 1, 0, -1, -1, -1, -1, -1, -1, 0, 1, 2, 1, 0, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -1, 0, 1, 2, 3, 2, 1, 0, -1, -2, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -2, -1, 0, 1, 2, 3, 4, 3, 2, 1, 0, -1, -2, -3, -4 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,13

COMMENTS

A329116 gives x-coordinates for a point moving in counterclockwise triangular spiral.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Index entries for sequences related to coordinates of 2D curves

FORMULA

a(n) = floor(min(s*max(((0, 2*s) mod 2) - 2), (-2*s*s) mod (-1)) + ceiling(-s/2)) where s=sqrt(n).

EXAMPLE

    y

     |

   4 |                         56

     |                           \

     |                            \

     |                             \

   3 |                         30  55

     |                         / \   \

     |                        /   \   \

     |                       /     \   \

   2 |                     31  12  29  54

     |                     /   / \   \   \

     |                    /   /   \   \   \

     |                   /   /     \   \   \

   1 |                 32  13   2  11  28  53

     |                 /   /   / \   \   \   \

     |                /   /   /   \   \   \   \

     |               /   /   /     \   \   \   \

   0 |             33  14   3   0---1  10  27  52

     |             /   /   /             \   \   \

     |            /   /   /               \   \   \

     |           /   /   /                 \   \   \

  -1 |         34  15   4---5---6---7---8---9  26  51

     |         /   /                             \   \

     |        /   /                               \   \

     |       /   /                                 \   \

  -2 |     35  16--17--18--19--20--21--22--23--24--25  50

     |     /                                             \

     |    /                                               \

     |   /                                                 \

  -3 | 36--37--38--39--40--41--42--43--44--45--46--47--48--49

     |

     +--------------------------------------------------------

   x:  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7

MATHEMATICA

a[n_] := Table[Floor[Min[#*Max[0, 2*Mod[#, 2] - 2], -2*#*Mod[#, -1]] + Ceiling[-#/2]] &[Sqrt@ k], {k, 0, n}]; a[64]

CROSSREFS

Cf. A268038, A274923.

Sequence in context: A030363 A236460 A029388 * A321005 A055254 A035670

Adjacent sequences:  A329969 A329970 A329971 * A329973 A329974 A329975

KEYWORD

sign,look

AUTHOR

Mikk Heidemaa, Nov 26 2019

STATUS

approved

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Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)