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A212511 Number of (w,x,y,z) with all terms in {1,...,n} and w<2x and y>=3z.

%I A212511 #8 Dec 18 2015 07:56:12
%S A212511 0,0,0,7,24,57,135,259,432,732,1125,1638,2376,3302,4410,5915,7680,
%T A212511 9765,12393,15447,18900,23170,27951,33348,39744,46900,54756,63999,
%U A212511 74088,85185,97875,111755,126720,143792,162129,181962,204120,227994,253422,281827,312000
%N A212511 Number of (w,x,y,z) with all terms in {1,...,n} and w<2x and y>=3z.
%C A212511 For a guide to related sequences, see A211795.
%H A212511 Colin Barker, <a href="/A212511/b212511.txt">Table of n, a(n) for n = 0..1000</a>
%H A212511 <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,2,-1,-4,0,2,0,-2,0,4,1,-2,-2,0,1).
%F A212511 a(n) = 2*a(n-2)+2*a(n-3)-a(n-4)-4*a(n-5)+2*a(n-7)-2*a(n-9)+4*a(n-11)+a(n-12)-2*a(n-13)-2*a(n-14)+a(n-16).
%F A212511 G.f.: x^3*(7 +24*x +43*x^2 +73*x^3 +104*x^4 +100*x^5 +97*x^6 +92*x^7 +61*x^8 +30*x^9 +14*x^10 +3*x^11) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3). - _Colin Barker_, Dec 18 2015
%t A212511 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212511 (Do[If[w < 2 x && y >= 3 z, s = s + 1],
%t A212511 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212511 Map[t[#] &, Range[0, 50]]   (* A212511 *)
%o A212511 (PARI) concat(vector(3), Vec(x^3*(7 +24*x +43*x^2 +73*x^3 +104*x^4 +100*x^5 +97*x^6 +92*x^7 +61*x^8 +30*x^9 +14*x^10 +3*x^11) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3) + O(x^60))) \\ _Colin Barker_, Dec 18 2015
%Y A212511 Cf. A211795, A212508, A212509, A212510.
%K A212511 nonn,easy
%O A212511 0,4
%A A212511 _Clark Kimberling_, May 20 2012