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A213391 Number of (w,x,y) with all terms in {0,...,n} and 2*max(w,x,y) < 3*min(w,x,y).

%I A213391 #29 Mar 13 2022 19:41:14
%S A213391 0,1,2,3,10,17,24,43,62,81,118,155,192,253,314,375,466,557,648,775,
%T A213391 902,1029,1198,1367,1536,1753,1970,2187,2458,2729,3000,3331,3662,3993,
%U A213391 4390,4787,5184,5653,6122,6591,7138,7685,8232,8863,9494,10125
%N A213391 Number of (w,x,y) with all terms in {0,...,n} and 2*max(w,x,y) < 3*min(w,x,y).
%C A213391 For a guide to related sequences, see A212959.
%C A213391 Also the number of (w,x,y) with all terms in {0,...,n-1} and 2*max(w,x,y) <= 3*min(w,x,y).
%H A213391 <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 A213391 a(n) + A213392(n) = (n+1)^3.
%F A213391 a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3) - 4*a(n-4) - a(n-5) + 2*a(n-6) - a(n-7).
%F A213391 G.f.: (x + 4*x^4 + x^7)/(((1 - x)^4)*(1 + x + x^2)^2).
%F A213391 a(n) = (n^3 + 6*n*(((n+1) mod 3 + 1) mod 2) - 2 + 2*((n+1) mod 3))/9. - _Ayoub Saber Rguez_, Feb 01 2022
%F A213391 From _Jon E. Schoenfield_, Feb 02 2022: (Start)
%F A213391 a(n) =  n^3/9            if n == 0 (mod 3),
%F A213391        (n^3 + 6*n + 2)/9 if n == 1 (mod 3),
%F A213391        (n^3 + 6*n - 2)/9 if n == 2 (mod 3).
%F A213391 (End)
%t A213391 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A213391 (Do[If[2*Max[w, x, y] < 3*Min[w, x, y], s = s + 1],
%t A213391 {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t A213391 m = Map[t[#] &, Range[0, 45]]   (* A213391 *)
%Y A213391 Cf. A212959, A213392.
%K A213391 nonn,easy
%O A213391 0,3
%A A213391 _Clark Kimberling_, Jun 11 2012