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A213502 Number of (w,x,y) with all terms in {0,...,n} and x != min(|w-x|, |x-y|).

%I A213502 #24 Oct 27 2024 06:11:21
%S A213502 0,4,17,47,98,178,291,445,644,896,1205,1579,2022,2542,3143,3833,4616,
%T A213502 5500,6489,7591,8810,10154,11627,13237,14988,16888,18941,21155,23534,
%U A213502 26086,28815,31729,34832,38132,41633,45343,49266,53410,57779
%N A213502 Number of (w,x,y) with all terms in {0,...,n} and x != min(|w-x|, |x-y|).
%C A213502 For a guide to related sequences, see A212959.
%H A213502 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-2,3,-1).
%F A213502 a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - a(n-5).
%F A213502 G.f.: x*(4 + 5*x + 4*x^2 - x^3)/((1 - x)^4*(1 + x)).
%F A213502 a(n) = (n+1)^3 - A213398(n).
%F A213502 a(n) = (2*n*(2*n^2+4*n+1) - (-1)^n + 1)/4. - _Bruno Berselli_, Jul 02 2012
%t A213502 t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[x != Min[Abs[w - x], Abs[x - y]], s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t A213502 m = Map[t[#] &, Range[0, 60]]
%Y A213502 Cf. A212959, A213398.
%K A213502 nonn,easy
%O A213502 0,2
%A A213502 _Clark Kimberling_, Jun 14 2012