A329972 - OEIS

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

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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

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