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A213389 Number of (w,x,y) with all terms in {0,...,n} and max(w,x,y) < 2*min(w,x,y).

%I A213389 #29 Jun 24 2025 11:29:12
%S A213389 0,1,2,9,16,35,54,91,128,189,250,341,432,559,686,855,1024,1241,1458,
%T A213389 1729,2000,2331,2662,3059,3456,3925,4394,4941,5488,6119,6750,7471,
%U A213389 8192,9009,9826,10745,11664,12691,13718,14859,16000,17261,18522
%N A213389 Number of (w,x,y) with all terms in {0,...,n} and max(w,x,y) < 2*min(w,x,y).
%C A213389 For a guide to related sequences, see A212959.
%H A213389 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).
%F A213389 a(n) = (n+1)^3 - A213390(n).
%F A213389 a(n) = 2*a(n-1)+a(n-2)-4*a(n-3)+a(n-4)+2*a(n-5)-a(n-6).
%F A213389 G.f.: (x + 4*x^3 + x^5)/((1 - x)^4*(1 + x)^2).
%F A213389 a(n) = n * ceiling(n^2/4). - _Wesley Ivan Hurt_, Jun 15 2013
%F A213389 a(n) = n*(2*n^2+3*(1-(-1)^n))/8. - _Luce ETIENNE_, Jul 17 2016
%t A213389 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A213389 (Do[If[Max[w, x, y] < 2*Min[w, x, y], s = s + 1],
%t A213389 {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t A213389 m = Map[t[#] &, Range[0, 50]]   (* A213389 *)
%t A213389 LinearRecurrence[{2,1,-4,1,2,-1},{0,1,2,9,16,35},50] (* _Harvey P. Dale_, Jun 24 2025 *)
%o A213389 (PARI) a(n)=n*ceil(n^2/4) \\ _Charles R Greathouse IV_, Jul 17 2016
%Y A213389 Cf. A212959.
%K A213389 nonn,easy
%O A213389 0,3
%A A213389 _Clark Kimberling_, Jun 11 2012