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A213499 Number of (w,x,y) with all terms in {0,...,n} and w != min(|w-x|, |x-y|).

%I A213499 #20 Feb 19 2024 11:42:44
%S A213499 0,4,17,47,96,176,286,439,634,885,1188,1561,1997,2515,3108,3796,4569,
%T A213499 5451,6429,7528,8735,10076,11535,13142,14878,16774,18811,21021,23382,
%U A213499 25930,28640,31549,34632,37927,41406,45111,49011,53149,57494
%N A213499 Number of (w,x,y) with all terms in {0,...,n} and w != min(|w-x|, |x-y|).
%C A213499 For a guide to related sequences, see A212959.
%H A213499 <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 A213499 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 A213499 G.f.: (x*(4 + 13*x + 22*x^2 + 19*x^3 + 11*x^4 + 3*x^5))/((-1 + x)^4 (1 + x)^2 (1 + x + x^2)).
%F A213499 a(n) = (n+1)^3 - A213497(n).
%t A213499 t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[w != Min[Abs[w - x], Abs[x - y]], s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t A213499 m = Map[t[#] &, Range[0, 60]]
%t A213499 LinearRecurrence[{1,2,-1,-2,-1,2,1,-1},{0,4,17,47,96,176,286,439},40] (* or *) CoefficientList[Series[(x (4+13 x+22 x^2+19 x^3+11 x^4+3 x^5))/((-1+x)^4 (1+x)^2 (1+x+x^2)),{x,0,40}],x] (* _Harvey P. Dale_, Sep 03 2021 *)
%Y A213499 Cf. A212959, A213497.
%K A213499 nonn,easy
%O A213499 0,2
%A A213499 _Clark Kimberling_, Jun 14 2012