A212108 Number of (w,x,y,z) with all terms in {1,...,n} and w*x-y*z<n.

0, 1, 13, 62, 187, 444, 885, 1616, 2677, 4227, 6326, 9163, 12742, 17468, 23167, 30278, 38876, 49268, 61315, 75858, 92363, 111867, 134039, 159426, 187841, 220810, 257093, 297936, 343312, 394178, 449481, 511840, 578961, 653514, 734486

Offset

0,3

Comments

A212108(n)+A211061(n)=n^4. For a guide to related sequences, see A211795.

Links

Table of n, a(n) for n=0..34.

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w*x < y*z + n, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 40]]   (* A212108 *)
(* Peter J. C. Moses, Apr 13 2012 *)

Crossrefs

Cf. A211795, A211061.

Sequence in context: A044151 A044532 A268201 * A213843 A031074 A285482

Adjacent sequences: A212105 A212106 A212107 * A212109 A212110 A212111

Keyword

nonn

Author

Clark Kimberling, May 07 2012

Status

approved