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A213496 Number of (w,x,y) with all terms in {0,...,n} and x != max(|w-x|,|x-y|).

%I A213496 #19 Jun 02 2025 08:02:43
%S A213496 0,4,13,41,82,158,255,403,580,824,1105,1469,1878,2386,2947,3623,4360,
%T A213496 5228,6165,7249,8410,9734,11143,12731,14412,16288,18265,20453,22750,
%U A213496 25274,27915,30799,33808,37076,40477,44153,47970,52078,56335
%N A213496 Number of (w,x,y) with all terms in {0,...,n} and x != max(|w-x|,|x-y|).
%C A213496 For a guide to related sequences, see A212959.
%H A213496 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).
%F A213496 a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6).
%F A213496 G.f.:  (4*x + 5*x^2 + 11*x^3 + 3*x^4 + x^5)/((1 - x)^4 (1 + x)^2).
%F A213496 From _Ayoub Saber Rguez_, Nov 20 2021: (Start)
%F A213496 a(n) = (n+1)^3 - A213399(n).
%F A213496 a(n) = (2*n^3 + 2*n^2 + 3*n + 1 - (2+n+1)*((n+1) mod 2))/2. (End)
%t A213496 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A213496 (Do[If[x != Max[Abs[w - x], Abs[x - y]], s = s + 1],
%t A213496 {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t A213496 m = Map[t[#] &, Range[0, 60]]   (* A213496 *)
%Y A213496 Cf. A212959, A213399.
%K A213496 nonn,easy
%O A213496 0,2
%A A213496 _Clark Kimberling_, Jun 14 2012