A212092 Number of (w,x,y,z) with all terms in {1,...,n} and w^2<x^2+y^2+z^2.

0, 1, 15, 73, 231, 562, 1155, 2133, 3632, 5801, 8830, 12907, 18264, 25131, 33766, 44461, 57524, 73274, 92043, 114213, 140173, 170289, 205057, 244884, 290251, 341658, 399594, 464582, 537200, 618046, 707665, 806727, 915828, 1035607

Offset

0,3

Comments

a(n)+A212095(n)=n^4.

For a guide to related sequences, see A211795.

Links

Table of n, a(n) for n=0..33.

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]] (* A212092 *)
(* Peter J. C. Moses, Apr 13 2012 *)

Crossrefs

Cf. A211795.

Sequence in context: A000476 A002603 A212562 * A022817 A171341 A080841

Adjacent sequences: A212089 A212090 A212091 * A212093 A212094 A212095

Keyword

nonn

Author

Clark Kimberling, May 02 2012

Status

approved