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A213492 Number of (w,x,y) with all terms in {0,...,n} and w != min(|w-x|, |x-y|, |y-w|).

%I A213492 #13 Feb 19 2024 10:27:15
%S A213492 0,4,18,48,98,178,290,442,640,890,1196,1568,2008,2524,3122,3808,4586,
%T A213492 5466,6450,7546,8760,10098,11564,13168,14912,16804,18850,21056,23426,
%U A213492 25970,28690,31594,34688,37978,41468,45168,49080,53212,57570
%N A213492 Number of (w,x,y) with all terms in {0,...,n} and w != min(|w-x|, |x-y|, |y-w|).
%C A213492 Every term is even.
%C A213492 For a guide to related sequences, see A212959.
%H A213492 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1,-1,0,2,-1).
%F A213492 a(n) = 2*a(n-1) - a(n-3) - a(n-4) + 2*a(n-6) - a(n-7).
%F A213492 G.f.: (2*x*(2 + 5*x + 6*x^2 + 3*x^3 + 2*x^4))/((-1 + x)^4 (1 + x) (1 + x + x^2)).
%F A213492 a(n) = (n+1)^3 - A213495(n).
%t A213492 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A213492 (Do[If[w != Min[Abs[w - x], Abs[x - y], Abs[y - w]], s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t A213492 m = Map[t[#] &, Range[0, 60]]   (* this sequence *)
%t A213492 m/2 (* integers *)
%Y A213492 Cf. A212959, A213495.
%K A213492 nonn,easy
%O A213492 0,2
%A A213492 _Clark Kimberling_, Jun 14 2012