A211639 Number of ordered triples (w,x,y) with all terms in {1,...,n} and w^2+x^2+y^2<=n.

0, 0, 0, 1, 1, 1, 4, 4, 4, 7, 7, 10, 11, 11, 17, 17, 17, 20, 23, 26, 26, 32, 35, 35, 38, 38, 44, 48, 48, 54, 60, 60, 60, 66, 69, 75, 78, 78, 87, 87, 87, 96, 102, 105, 108, 114, 120, 120, 121, 127, 133, 139, 139, 145, 157, 157, 163, 169, 169, 178, 178, 184, 196

Offset: 0

Author

Clark Kimberling, Apr 18 2012

Keywords

• nonn

Comments

For a guide to related sequences, see A211422.

Crossrefs

Cf. A211638, A211422. Partial sums of A063691.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
    (Do[If[w^2 + x^2 + y^2 <= n, s = s + 1],
        {w, 1, #}, {x, 1, #}, {y, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 80]]     (* A211639 *)
(* Peter J. C. Moses, Apr 13 2012 *)

Formula

a(n) = A211638(n)+A063691(n). - R. J. Mathar, Jan 07 2015

G.f.: (theta_3(x) - 1)^3/(8*(1 - x)), where theta_3() is the Jacobi theta function. - Ilya Gutkovskiy, Apr 17 2018