A212104 Number of (w,x,y,z) with all terms in {1,...,n} and w <= harmonic mean of {x,y,z}.

0, 1, 9, 36, 106, 252, 528, 964, 1617, 2559, 3880, 5631, 7950, 10900, 14595, 19161, 24727, 31419, 39399, 48790, 59799, 72570, 87277, 104124, 123342, 145075, 169575, 197061, 227779, 261915, 299778, 341599, 387624, 438171, 493486

Offset: 0

Author

Clark Kimberling, May 04 2012

Keywords

• nonn

Comments

a(n)+A212105(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, 50]] (* A212104 *)
FindLinearRecurrence[%]
(* Peter J. C. Moses, Apr 13 2012 *)