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A213501 Number of (w,x,y) with all terms in {0,...,n} and w != max(|w-x|, |x-y|).

%I A213501 #27 Oct 27 2024 06:11:17
%S A213501 0,4,16,45,94,172,281,433,626,875,1177,1547,1981,2497,3087,3772,4543,
%T A213501 5421,6396,7492,8695,10032,11488,13090,14822,16714,18746,20951,23308,
%U A213501 25850,28555,31459,34536,37825,41299,44997,48891,53023,57361,61950,66757,71827
%N A213501 Number of (w,x,y) with all terms in {0,...,n} and w != max(|w-x|, |x-y|).
%C A213501 For a guide to related sequences, see A212959.
%H A213501 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-1,-2,-1,2,1,-1).
%F A213501 a(n) = a(n-1) + 2*a(n-2) - a(n-3) - 2*a(n-4) - a(n-5) + 2*a(n-6) + a(n-7) - a(n-8).
%F A213501 G.f.: x*(4 + 12*x + 21*x^2 + 21*x^3 + 12*x^4 + 2*x^5)/((1 - x)^4*(1 + x)^2*(1 + x + x^2)).
%F A213501 a(n) = (n+1)^3 - A213395(n).
%F A213501 a(n) = (6*n*(n+1)*(24*n+17) - 9*(2*n+1)*(-1)^n + 32*cos(2*Pi*(n+2)/3) + 25)/144. - _Bruno Berselli_, Jul 02 2012
%t A213501 t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[w != Max[Abs[w - x], Abs[x - y]], s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t A213501 m = Map[t[#] &, Range[0, 60]]
%t A213501 LinearRecurrence[{1,2,-1,-2,-1,2,1,-1},{0,4,16,45,94,172,281,433},50] (* _Harvey P. Dale_, Oct 01 2021 *)
%Y A213501 Cf. A212959, A213395.
%K A213501 nonn,easy
%O A213501 0,2
%A A213501 _Clark Kimberling_, Jun 14 2012