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A213498 Number of (w,x,y) with all terms in {0,...,n} and w != max(|w-x|,|x-y|,|y-w|).

%I A213498 #22 Jun 02 2025 08:02:49
%S A213498 0,4,15,43,88,164,267,415,600,844,1135,1499,1920,2428,3003,3679,4432,
%T A213498 5300,6255,7339,8520,9844,11275,12863,14568,16444,18447,20635,22960,
%U A213498 25484,28155,31039,34080,37348,40783,44459,48312,52420,56715
%N A213498 Number of (w,x,y) with all terms in {0,...,n} and w != max(|w-x|,|x-y|,|y-w|).
%C A213498 a(n)+A212965 = (n+1)^3.
%C A213498 For a guide to related sequences, see A212959.
%H A213498 Harvey P. Dale, <a href="/A213498/b213498.txt">Table of n, a(n) for n = 0..1000</a>
%H A213498 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).
%F A213498 a(n) = 2*a(n-1)+a(n-2)-4*a(n-3)+a(n-4)+2*a(n-5)-a(n-6).
%F A213498 G.f.: (4*x + 7*x^2 + 9*x^3 + 3*x^4 + x^5)/((-1 + x)^4*(1 + x)^2).
%F A213498 a(n) = (2*n*(4*n^2+5*n+5) - (2*n+1)*(-1)^n + 1)/8.
%t A213498 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A213498 (Do[If[w != Max[Abs[w - x], Abs[x - y], Abs[y - w]], s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t A213498 m = Map[t[#] &, Range[0, 60]]   (* A213498 *)
%t A213498 LinearRecurrence[{2,1,-4,1,2,-1},{0,4,15,43,88,164},50] (* _Harvey P. Dale_, Mar 27 2020 *)
%Y A213498 Cf. A212959.
%K A213498 nonn,easy
%O A213498 0,2
%A A213498 _Clark Kimberling_, Jun 14 2012