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A213393 Number of (w,x,y) with all terms in {0,...,n} and 2*max(w,x,y) > 3*min(w,x,y).

%I A213393 #25 Feb 25 2023 08:31:49
%S A213393 0,6,24,54,108,192,300,450,648,882,1176,1536,1944,2430,3000,3630,4356,
%T A213393 5184,6084,7098,8232,9450,10800,12288,13872,15606,17496,19494,21660,
%U A213393 24000,26460,29106,31944,34914,38088,41472,45000,48750,52728
%N A213393 Number of (w,x,y) with all terms in {0,...,n} and 2*max(w,x,y) > 3*min(w,x,y).
%C A213393 Every term is even.
%C A213393 For a guide to related sequences, see A212959.
%H A213393 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,2,-4,2,-1,2,-1).
%F A213393 a(n) + A213391(n+1) = (n+1)^3.
%F A213393 a(n) = 2*a(n-1)-a(n-2)+2*a(n-3)-4*a(n-4)+2*a(n-5)-a(n-6)+2*a(n-7)-a(n-8).
%F A213393 G.f.: 6*x*(x^2+1)*(x+1)^2 / ((x^2+x+1)^2*(x-1)^4).
%F A213393 From _Ayoub Saber Rguez_, Feb 01 2022: (Start)
%F A213393 a(n) = 6*A190798(n+1).
%F A213393 a(n) = A213392(n) - A092076(n).
%F A213393 a(n) = (8*n^2+16*n+8-8*n*((2*n+2) mod 3)-8*((2*n+2) mod 3)+2*((2*n+2) mod 3)^2)/3. (End)
%F A213393 E.g.f.: 2*exp(-x/2)*(6*exp(3*x/2)*(1 + x*(13 + 2*x*(6 + x))) - 3*(2 + x)*cos(sqrt(3)*x/2) - sqrt(3)*(2 - 3*x)*sin(sqrt(3)*x/2))/27. - _Stefano Spezia_, Feb 25 2023
%t A213393 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A213393 (Do[If[2*Max[w, x, y] > 3*Min[w, x, y], s = s + 1],
%t A213393 {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t A213393 m = Map[t[#] &, Range[0, 45]]   (* A213393 *)
%t A213393 m/2   (* integers *)
%Y A213393 Cf. A212959, A213391.
%Y A213393 Cf. A092076, A190798, A213392.
%K A213393 nonn,easy
%O A213393 0,2
%A A213393 _Clark Kimberling_, Jun 11 2012