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

%I A212104 #8 Dec 04 2016 19:46:29
%S A212104 0,1,9,36,106,252,528,964,1617,2559,3880,5631,7950,10900,14595,19161,
%T A212104 24727,31419,39399,48790,59799,72570,87277,104124,123342,145075,
%U A212104 169575,197061,227779,261915,299778,341599,387624,438171,493486
%N A212104 Number of (w,x,y,z) with all terms in {1,...,n} and w <= harmonic mean of {x,y,z}.
%C A212104 a(n)+A212105(n)=n^4.
%C A212104 A 4-tuple (w,x,y,z) is counted if 3/w<=1/x+1/y+1/z.
%C A212104 For a guide to related sequences, see A211795.
%t A212104 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212104 (Do[If[w*(y*z + z*x + x*y) <= 3 x*y*z, s = s + 1],
%t A212104 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212104 Map[t[#] &, Range[0, 50]] (* A212104 *)
%t A212104 FindLinearRecurrence[%]
%t A212104 (* _Peter J. C. Moses_, Apr 13 2012 *)
%Y A212104 Cf. A211795, A212103.
%K A212104 nonn
%O A212104 0,3
%A A212104 _Clark Kimberling_, May 04 2012