A212255 Number of (w,x,y,z) with all terms in {1,...,n} and 3w^2 = x^2 + y^2 + z^2.

0, 1, 2, 3, 4, 8, 9, 16, 17, 18, 22, 32, 33, 43, 50, 54, 55, 68, 69, 85, 89, 96, 106, 125, 126, 151, 161, 162, 169, 191, 195, 220, 221, 231, 244, 284, 285, 313, 329, 339, 343, 380, 387, 415, 425, 429, 448, 485, 486, 523, 548, 561, 571, 611, 612, 685, 692

Offset: 0

Author

Clark Kimberling, May 15 2012

Keywords

• nonn

Comments

w^2 = average of x^2, y^2, z^2. For a guide to related sequences, see A211795.

Crossrefs

Cf. A211795.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[3 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, 60]]  (* A212255 *)
(* Peter J. C. Moses, Apr 13 2012 *)