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

Offset: 0

Author

M. F. Hasler, Apr 28 2021

Keywords

• sign
• tabf

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

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).

Programs

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.