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A213482 Number of (w,x,y) with all terms in {0,...,n} and |w-x| + |x-y| > w+x+y.

%I A213482 #23 Oct 27 2024 06:11:07
%S A213482 0,3,14,41,87,161,265,409,594,831,1120,1473,1889,2381,2947,3601,4340,
%T A213482 5179,6114,7161,8315,9593,10989,12521,14182,15991,17940,20049,22309,
%U A213482 24741,27335,30113,33064,36211,39542,43081,46815,50769,54929
%N A213482 Number of (w,x,y) with all terms in {0,...,n} and |w-x| + |x-y| > w+x+y.
%C A213482 For a guide to related sequences, see A212959.
%H A213482 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).
%F A213482 a(n) + A213483(n) = (n+1)^3.
%F A213482 a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6).
%F A213482 G.f.: (3*x + 8*x^2 + 10*x^3 + 3*x^4 - x^5)/((1 - x)^4*(1 + x)^2).
%F A213482 From _Ayoub Saber Rguez_, Dec 29 2021: (Start)
%F A213482 a(n) = A213481(n) - A213479(n).
%F A213482 a(n) = (23*n^3 + 39*n^2 + n + 9 - (3*n+9)*((n+1) mod 2))/24. (End)
%t A213482 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A213482 (Do[If[w + x + y > Abs[w - x] + Abs[x - y], s = s + 1],
%t A213482 {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t A213482 Map[t[#] &, Range[0, 60]]   (* A213482 *)
%Y A213482 Cf. A212959, A213479, A213481, A213483.
%K A213482 nonn,easy
%O A213482 0,2
%A A213482 _Clark Kimberling_, Jun 13 2012