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A213399 Number of (w,x,y) with all terms in {0,...,n} and max(|w-x|,|x-y|) = x.

%I A213399 #13 Jul 25 2024 20:56:58
%S A213399 1,4,14,23,43,58,88,109,149,176,226,259,319,358,428,473,553,604,694,
%T A213399 751,851,914,1024,1093,1213,1288,1418,1499,1639,1726,1876,1969,2129,
%U A213399 2228,2398,2503,2683,2794,2984,3101,3301,3424,3634,3763,3983,4118
%N A213399 Number of (w,x,y) with all terms in {0,...,n} and max(|w-x|,|x-y|) = x.
%C A213399 For a guide to related sequences, see A212959.
%H A213399 Colin Barker, <a href="/A213399/b213399.txt">Table of n, a(n) for n = 0..1000</a>
%H A213399 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A213399 a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5).
%F A213399 G.f.: (1 + 3*x + 8*x^2 + 3*x^3 + x^4)/((1 - x)^3 * (1 + x)^2).
%F A213399 From _Colin Barker_, Jan 26 2016: (Start)
%F A213399 a(n) = (8*n^2+2*(-1)^n*n+8*n+(-1)^n+3)/4.
%F A213399 a(n) = (4*n^2+5*n+2)/2 for n even.
%F A213399 a(n) = (4*n^2+3*n+1)/2 for n odd.
%F A213399 (End)
%t A213399 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A213399 (Do[If[x == Max[Abs[w - x], Abs[x - y]], s = s + 1],
%t A213399 {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t A213399 Map[t[#] &, Range[0, 60]]   (* A213399 *)
%o A213399 (PARI) Vec((1+3*x+8*x^2+3*x^3+x^4) / ((1-x)^3*(1+x)^2) + O(x^100)) \\ _Colin Barker_, Jan 26 2016
%Y A213399 Cf. A212959.
%K A213399 nonn,easy
%O A213399 0,2
%A A213399 _Clark Kimberling_, Jun 13 2012