A343633 Z-coordinate of the points following the 3D spiral defined in A343630.

0, 1, 0, 0, 0, 0, -1, -1, -1, -1, -1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -2, -2, -2, -2, -3, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, 0

Offset: 0

Author

M. F. Hasler, Apr 28 2021

Keywords

• sign

Comments

See the main entry A343630 for details about this 3D generalization of an Ulam type spiral using the Euclidean norm.

Sequences A343631 and A343632 give the x and y-coordinates.

The sequence can be seen as a table with row lengths A005875, where A005875(r) is the number of points at distance sqrt(r) from the origin.

Sequence A343643 is the analog for the square spiral variant A343640.

Crossrefs

Cf. A343631, A343633 (list of x and z-coordinates).

Cf. A343643 (variant using the sup norm => square spiral).

Cf. A342563 (variant which scans each sphere by increasing z).

Cf. A005875 (number of points on a shell with given radius).

Cf. A004215 (numbers that can't be written as sum of 3 squares => empty shells).

Programs

PARI

d=1; A343633_vec=concat([[P[3] | P<-S=A343630_row(n,d)]+(#S&&!d*=-1) | n<-[0..9]]) \\ the variable d is necessary to correct the z-scan direction in rows between A004215(2k-1) and A004215(2k).