A343643 - OEIS

A343643

Z-coordinate of points following the 3D square spiral defined in A343640.

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,28

COMMENTS

See A343640 for more information about this 3D generalization of the 2D Ulam type square spiral.

The sequence can be seen as a table with row lengths A010014, where A010014(r) is the number of points of Z^3 with sup-norm r.

The graph of this sequence oscillates with increasing amplitude and wave length.

LINKS

Hugo Pfoertner, Table of n, a(n) for n = 0..9260

PROG

(PARI) A343643_vec=concat([[P[3]| P<-A343640_row(n)] | n<-[0..2]]) \\ From 0 up to n there are (2n+1)^3 points with 3 coordinates each.

CROSSREFS

Cf. A343640 (triples), A343641 and A343642 (list of X and Y-coordinates).

Cf. A343633 (variant using the Euclidean norm), A342563 (another variant).

Cf. A010014 (number of points on a shell with given radius => row lengths).

Sequence in context: A194294 A263110 A044927 * A044928 A362114 A274070

Adjacent sequences: A343640 A343641 A343642 * A343644 A343645 A343646

KEYWORD

sign,tabf

AUTHOR

M. F. Hasler, Apr 28 2021

STATUS

approved