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A212740 Number of (w,x,y,z) with all terms in {0,...,n} and max{w,x,y,z}<2*min{w,x,y,z}.

%I A212740 #15 Jun 13 2015 00:54:14
%S A212740 0,1,2,17,32,97,162,337,512,881,1250,1921,2592,3697,4802,6497,8192,
%T A212740 10657,13122,16561,20000,24641,29282,35377,41472,49297,57122,66977,
%U A212740 76832,89041,101250,116161,131072,149057,167042,188497,209952
%N A212740 Number of (w,x,y,z) with all terms in {0,...,n} and max{w,x,y,z}<2*min{w,x,y,z}.
%C A212740 a(n)+A212741(n)=n^4.  For a guide to related sequences, see A211795.
%H A212740 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-6,0,6,-2,-2,1).
%F A212740 a(n) = 2*a(n-1)+2*a(n-2)-6*a(n-3)+6*a(n-5)-2*a(n-6)-2*a(n-7)+a(n-8).
%F A212740 G.f.: -x*(1+x^2)*(x^4+10*x^2+1) / ( (1+x)^3*(x-1)^5 ).
%F A212740 a(n) = 3*n^2/8 +1/16 +n^4/8 -(-1)^n/16 -3*(-1)^n*n^2/8. - _R. J. Mathar_, Jul 01 2013
%t A212740 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212740 (Do[If[Max[w, x, y, z] < 2 Min[w, x, y, z], s = s + 1],
%t A212740 {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
%t A212740 Map[t[#] &, Range[0, 40]]   (* A212740 *)
%Y A212740 Cf. A211795.
%K A212740 nonn,easy
%O A212740 0,3
%A A212740 _Clark Kimberling_, May 26 2012