A212111 Number of (w,x,y,z) with all terms in {1,...,n} and w*x+y*z<n^2.

0, 0, 5, 48, 180, 481, 1034, 1986, 3441, 5602, 8623, 12755, 18126, 25165, 33951, 44936, 58367, 74638, 93934, 116987, 143760, 175126, 211253, 252782, 299884, 353673, 414098, 482057, 557997, 642810, 736317, 840479, 954638, 1080451

Offset

0,3

Comments

A212111(n)+A212132(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, 60]]   (* A212111 *)
(* Peter J. C. Moses, Apr 13 2012 *)

Crossrefs

Cf. A211795.

Sequence in context: A291863 A247705 A215543 * A359969 A215050 A268785

Adjacent sequences: A212108 A212109 A212110 * A212112 A212113 A212114

Keyword

nonn

Author

Clark Kimberling, May 07 2012

Status

approved