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A212970 Number of (w,x,y) with all terms in {0,...,n} and w != x and x < range(w,x,y).

%I A212970 #26 Apr 17 2023 15:57:21
%S A212970 0,2,8,22,44,80,128,196,280,390,520,682,868,1092,1344,1640,1968,2346,
%T A212970 2760,3230,3740,4312,4928,5612,6344,7150,8008,8946,9940,11020,12160,
%U A212970 13392,14688,16082,17544,19110,20748,22496,24320,26260,28280
%N A212970 Number of (w,x,y) with all terms in {0,...,n} and  w != x and x < range(w,x,y).
%C A212970 For a guide to related sequences, see A212959.
%C A212970 Twice the partial sums of A210977. - _J. M. Bergot_, Aug 10 2013
%H A212970 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).
%F A212970 a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6).
%F A212970 G.f.: f(x)/g(x), where f(x) = 2*x*(1 + 2*x + 2*x^2) and g(x) = ((1-x)^4)(1+x)^2.
%F A212970 a(n) = 2 * A088003(n) for n>0.
%F A212970 From _Ayoub Saber Rguez_, Mar 31 2023: (Start)
%F A212970 a(n) + A212969(n+1) = A045991(n+1).
%F A212970 a(n) = (10*n^3 + 24*n^2 + 8*n + (6*n)*(n mod 2))/24. (End)
%t A212970 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212970 (Do[If[w != x < (Max[w, x, y] - Min[w, x, y]),
%t A212970    s = s + 1],
%t A212970 {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t A212970 m = Map[t[#] &, Range[0, 60]]   (* A212970 *)
%t A212970 m/2 (* essentially A088003 *)
%Y A212970 Cf. A088003, A210977, A212959.
%Y A212970 Cf. A045991, A212969.
%K A212970 nonn,easy
%O A212970 0,2
%A A212970 _Clark Kimberling_, Jun 02 2012
%E A212970 Typo in name corrected by _Ayoub Saber Rguez_, Mar 31 2023