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A212519 Number of (w,x,y,z) with all terms in {1,...,n} and w>2x and y>=3z.

%I A212519 #8 Dec 11 2015 10:44:12
%S A212519 0,0,0,1,4,12,30,63,108,192,300,450,660,936,1260,1715,2240,2880,3672,
%T A212519 4617,5670,7000,8470,10164,12144,14400,16848,19773,22932,26460,30450,
%U A212519 34875,39600,45056,50864,57222,64260,71928,80028,89167,98800,109200,120540
%N A212519 Number of (w,x,y,z) with all terms in {1,...,n} and w>2x and y>=3z.
%C A212519 For a guide to related sequences, see A211795.
%H A212519 Colin Barker, <a href="/A212519/b212519.txt">Table of n, a(n) for n = 0..1000</a>
%H A212519 <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 A212519 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 A212519 G.f.: x^3*(1 +4*x +10*x^2 +20*x^3 +32*x^4 +32*x^5 +34*x^6 +34*x^7 +25*x^8 +14*x^9 +8*x^10 +2*x^11) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3). - _Colin Barker_, Dec 11 2015
%t A212519 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212519 (Do[If[w > 2 x && y >= 3 z, s = s + 1],
%t A212519 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212519 Map[t[#] &, Range[0, 50]]   (* A212519 *)
%o A212519 (PARI) concat(vector(3), Vec(x^3*(1 +4*x +10*x^2 +20*x^3 +32*x^4 +32*x^5 +34*x^6 +34*x^7 +25*x^8 +14*x^9 +8*x^10 +2*x^11) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3) + O(x^100))) \\ _Colin Barker_, Dec 11 2015
%Y A212519 Cf. A211795, A212508.
%K A212519 nonn,easy
%O A212519 0,5
%A A212519 _Clark Kimberling_, May 20 2012