A329972 Y-coordinate of a point moving in a triangular spiral.

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

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