A212106 Number of (w,x,y,z) with all terms in {1,...,n} and w < harmonic mean of {x,y,z}.

0, 0, 7, 33, 96, 241, 498, 933, 1579, 2520, 3828, 5578, 7866, 10815, 14509, 19044, 24603, 31294, 39255, 48645, 59599, 72345, 87051, 103897, 123060, 144792, 169291, 196776, 227445, 261580, 299358, 341178, 387196, 437736, 493050

Offset: 0

Author

Clark Kimberling, May 04 2012

Keywords

• nonn

Comments

a(n)+A212107(n)=n^4.

A 4-tuple (w,x,y,z) is counted if 3/w<1/x+1/y+1/z.

For a guide to related sequences, see A211795.

Crossrefs

Cf. A211795, A212103.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w*(y*z + z*x + x*y) < 3 x*y*z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 40]] (* A212106 *)
(* Peter J. C. Moses, Apr 13 2012 *)