A212091 Number of (w,x,y,z) with all terms in {1,...,n} and w^2=x^2+y^2+z^2.

0, 0, 0, 3, 3, 3, 6, 12, 12, 24, 24, 33, 36, 42, 48, 63, 63, 72, 84, 99, 99, 132, 141, 159, 162, 174, 180, 219, 225, 243, 258, 282, 282, 330, 339, 369, 381, 405, 420, 465, 465, 492, 525, 558, 567, 627, 645, 681, 684, 732, 744, 804, 810, 846, 885, 930

Offset: 0

Author

Clark Kimberling, May 02 2012

Keywords

• nonn

Comments

Every term is divisible by 3. For a guide to related sequences, see A211795.

Crossrefs

Cf. A211795.

Partial sums of A181787.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w^2 == x^2 + y^2 + z^2, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 50]] (* A212091 *)
%/3  (* integers *)
(* Peter J. C. Moses, Apr 13 2012 *)