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%I #26 Mar 13 2022 19:41:32
%S 1,7,25,61,115,199,319,469,667,919,1213,1573,2005,2491,3061,3721,4447,
%T 5275,6211,7225,8359,9619,10969,12457,14089,15823,17713,19765,21931,
%U 24271,26791,29437,32275,35311,38485,41869,45469,49219,53197
%N Number of (w,x,y) with all terms in {0,...,n} and 2*max(w,x,y) >= 3*min(w,x,y).
%C For a guide to related sequences, see A212959.
%H <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 a(n) + A213391(n) = (n+1)^3.
%F 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 G.f.: -(-1 - 5*x - x^6 - 12*x^2 - 16*x^3 - 8*x^4 - 6*x^5 + x^7) / ((x^2 + x + 1)^2*(x-1)^4).
%F From _Ayoub Saber Rguez_, Feb 01 2022: (Start)
%F a(n) = A213393(n) + A092076(n).
%F a(n) = (8*n^3 + 27*n^2 + 21*n + 6*n*(((n+1) mod 3) mod 2) + 7 + 2*((2*n+1) mod 3))/9. (End)
%F From _Jon E. Schoenfield_, Feb 02 2022: (Start)
%F a(n) = (8*n^3 + 27*n^2 + 27*n + 9)/9 if n == 0 (mod 3);
%F = (8*n^3 + 27*n^2 + 21*n + 7)/9 if n == 1 (mod 3);
%F = (8*n^3 + 27*n^2 + 21*n + 11)/9 if n == 2 (mod 3).
%F (End)
%t t = Compile[{{n, _Integer}}, Module[{s = 0},
%t (Do[If[2*Max[w, x, y] >= 3*Min[w, x, y], s = s + 1],
%t {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t m = Map[t[#] &, Range[0, 45]] (* A213391 *)
%Y Cf. A212959, A213391.
%K nonn,easy
%O 0,2
%A _Clark Kimberling_, Jun 11 2012
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