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Number of (w,x,y,z) with all terms in {1,...,n} and w <= (geometric mean of x,y,z).
2

%I #5 Dec 04 2016 19:46:30

%S 0,1,9,39,121,285,579,1069,1815,2904,4396,6417,9060,12448,16704,21969,

%T 28414,36153,45393,56272,69012,83814,100888,120447,142692,167944,

%U 196341,228231,263815,303435,347295,395794,449244,507867,572014

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

%C A212143(n)+A212144(n)=n^4. For a guide to related sequences, see A211795.

%t t = Compile[{{n, _Integer}}, Module[{s = 0},

%t (Do[If[w^3 <= x*y*z, s = s + 1],

%t {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];

%t Map[t[#] &, Range[0, 50]] (* A212143 *)

%t (* _Peter J. C. Moses_, Apr 13 2012 *)

%Y Cf. A211795.

%K nonn

%O 0,3

%A _Clark Kimberling_, May 06 2012