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A212969 Number of (w,x,y) with all terms in {0,...,n} and w != x and x > range(w,x,y).

%I A212969 #28 Jun 07 2023 09:45:40
%S A212969 0,0,2,10,26,56,100,166,252,368,510,690,902,1160,1456,1806,2200,2656,
%T A212969 3162,3738,4370,5080,5852,6710,7636,8656,9750,10946,12222,13608,15080,
%U A212969 16670,18352,20160,22066,24106,26250,28536,30932,33478,36140
%N A212969 Number of (w,x,y) with all terms in {0,...,n} and w != x and x > range(w,x,y).
%C A212969 For a guide to related sequences, see A212959.
%H A212969 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).
%F A212969 a(n) = (n-1)*(2*n*(7*n-2) - 3*(-1)^n + 3)/24.
%F A212969 a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6).
%F A212969 G.f.: f(x)/g(x), where f(x) = 2*(x^2)*(1 + 3*x + 2*x^2 + x^3) and g(x) = ((1-x)^4)*(1+x)^2.
%F A212969 a(n) = A045991(n) - A212970(n-1). - _Ayoub Saber Rguez_, Mar 31 2023
%t A212969 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212969 (Do[If[w != x > (Max[w, x, y] - Min[w, x, y]),
%t A212969   s = s + 1],
%t A212969 {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t A212969 m = Map[t[#] &, Range[0, 60]]   (* A212969 *)
%t A212969 m/2 (* integers *)
%Y A212969 Cf. A212959, A045991, A212970.
%K A212969 nonn,easy
%O A212969 0,3
%A A212969 _Clark Kimberling_, Jun 02 2012