A212105 Number of (w,x,y,z) with all terms in {1,...,n} and w > harmonic mean of {x,y,z}.

0, 0, 7, 45, 150, 373, 768, 1437, 2479, 4002, 6120, 9010, 12786, 17661, 23821, 31464, 40809, 52102, 65577, 81531, 100201, 121911, 146979, 175717, 208434, 245550, 287401, 334380, 386877, 445366, 510222, 581922, 660952, 747750, 842850

Offset: 0

Author

Clark Kimberling, May 04 2012

Keywords

• nonn

Comments

a(n)+A212104(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]] (* A212105 *)
(* Peter J. C. Moses, Apr 13 2012 *)