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A213045 Number of (w,x,y) with all terms in {0,...,n} and 2*|w-x| > max(w,x,y) - min(w,x,y).

%I A213045 #25 Feb 19 2024 12:10:31
%S A213045 0,4,14,36,72,128,206,312,448,620,830,1084,1384,1736,2142,2608,3136,
%T A213045 3732,4398,5140,5960,6864,7854,8936,10112,11388,12766,14252,15848,
%U A213045 17560,19390,21344,23424,25636,27982,30468,33096,35872,38798,41880
%N A213045 Number of (w,x,y) with all terms in {0,...,n} and 2*|w-x| > max(w,x,y) - min(w,x,y).
%C A213045 Every term is even.
%H A213045 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-2,3,-1).
%F A213045 a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - a(n-5).
%F A213045 G.f.: 2*x*(2 + x + x^2)/((-1 + x)^4*(1 + x)).
%F A213045 a(n) = (n+1)^3 - A087035(n+1).
%F A213045 a(n) = 2*A212685(n+1) = (2*n*(4*n^2+9*n+8) - 3*(-1)^n + 3)/12. [_Bruno Berselli_, Jun 11 2012]
%t A213045 t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[Max[w, x, y] - Min[w, x, y] < 2 Abs[w - x], s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t A213045 m = Map[t[#] &, Range[0, 45]]   (* this sequence *)
%t A213045 m/2  (* integers *)
%t A213045 LinearRecurrence[{3,-2,-2,3,-1},{0,4,14,36,72},50] (* _Harvey P. Dale_, Jul 31 2013 *)
%Y A213045 See A212959 for a guide to related sequences.
%Y A213045 Cf. A087035, A212685.
%K A213045 nonn,easy
%O A213045 0,2
%A A213045 _Clark Kimberling_, Jun 10 2012