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%I #7 Jun 01 2022 18:13:09
%S 0,0,0,1,0,-1,0,0,1,0,-1,1,1,-1,-1,0,1,0,-1,1,1,-1,-1,1,1,-1,-1,0,0,2,
%T 0,-2,0,0,1,0,-1,0,2,0,-2,1,2,2,1,-1,-2,-2,-1,0,2,0,-2,1,-1,0,0,1,1,
%U -1,-1,1,2,2,1,-1,-2,-2,-1,1,2,2,1,-1,-2,-2,-1,1,1,-1,-1,0,2,0,-2,2,2,-2,-2,0,2,0,-2,0,1,2,2,1,-1,-2,-2,-1,2,2,-2,-2,0,3,0,-3
%N Y-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 A343633 give the x and z 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 A343642 is the analog for the square spiral variant A343640.
%o (PARI) d=1; A343632_vec=concat([[P[2] | 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. A343642 (variant using the sup norm => square spiral).
%Y Cf. A342562 (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 0,30
%A _M. F. Hasler_, Apr 28 2021