A212095 Number of (w,x,y,z) with all terms in {1,...,n} and w^2>=x^2+y^2+z^2.

0, 0, 1, 8, 25, 63, 141, 268, 464, 760, 1170, 1734, 2472, 3430, 4650, 6164, 8012, 10247, 12933, 16108, 19827, 24192, 29199, 34957, 41525, 48967, 57382, 66859, 77456, 89235, 102335, 116794, 132748, 150314, 169545, 190574, 213490, 238420

Offset

0,4

Comments

a(n)+A212092(n)=n^4. For a guide to related sequences, see A211795.

Links

Table of n, a(n) for n=0..37.

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]] (* A212095 *)
(* Peter J. C. Moses, Apr 13 2012 *)

Crossrefs

Cf. A211795.

Partial sums of A253663.

Sequence in context: A346522 A244834 A169831 * A287120 A127813 A295911

Adjacent sequences: A212092 A212093 A212094 * A212096 A212097 A212098

Keyword

nonn

Author

Clark Kimberling, May 02 2012

Status

approved