%I #12 Jun 01 2022 16:59:49

%S 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,

%T 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,

%U -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

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

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

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

%C 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.

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

%o (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).

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

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

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

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

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

%K sign

%O 0,28

%A _M. F. Hasler_, Apr 28 2021