A212150 Number of (w,x,y,z) with all terms in {1,...,n} and w*x+y*z<=n^2.

0, 0, 9, 56, 196, 499, 1074, 2014, 3497, 5658, 8705, 12811, 18278, 25239, 34099, 45086, 58543, 74748, 94210, 117123, 144094, 175386, 211549, 252962, 300400, 353941, 414476, 482417, 558525, 643076, 737167, 840779, 955262, 1080987

Offset

0,3

Comments

A212150(n)+A212136(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*x + y*z <= n^2, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 40]]  (* A212150 *)
(* Peter J. C. Moses, Apr 13 2012 *)

Crossrefs

Cf. A211795.

Sequence in context: A368889 A245488 A242604 * A203838 A097556 A196861

Adjacent sequences: A212147 A212148 A212149 * A212151 A212152 A212153

Keyword

nonn

Author

Clark Kimberling, May 07 2012

Status

approved