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A212518 Number of (w,x,y,z) with all terms in {1,...,n} and w>2x and y>3z.

%I A212518 #8 Dec 11 2015 10:44:01
%S A212518 0,0,0,0,2,8,18,45,84,144,240,375,540,792,1092,1470,1960,2560,3240,
%T A212518 4131,5130,6300,7700,9317,11088,13248,15600,18252,21294,24696,28350,
%U A212518 32625,37200,42240,47872,54043,60588,68040,75924,84474,93860,104000,114660,126567
%N A212518 Number of (w,x,y,z) with all terms in {1,...,n} and w>2x and y>3z.
%C A212518 For a guide to related sequences, see A211795.
%H A212518 Colin Barker, <a href="/A212518/b212518.txt">Table of n, a(n) for n = 0..1000</a>
%H A212518 <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 A212518 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 A212518 G.f.: x^4*(2 +8*x +14*x^2 +25*x^3 +34*x^4 +34*x^5 +32*x^6 +32*x^7 +20*x^8 +10*x^9 +4*x^10 +x^11) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3). - _Colin Barker_, Dec 11 2015
%t A212518 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212518 (Do[If[w > 2 x && y > 3 z, s = s + 1],
%t A212518 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212518 Map[t[#] &, Range[0, 50]]   (* A212518 *)
%o A212518 (PARI) concat(vector(4), Vec(x^4*(2 +8*x +14*x^2 +25*x^3 +34*x^4 +34*x^5 +32*x^6 +32*x^7 +20*x^8 +10*x^9 +4*x^10 +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 A212518 Cf. A211795, A212508.
%K A212518 nonn,easy
%O A212518 0,5
%A A212518 _Clark Kimberling_, May 20 2012