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A213495 Number of (w,x,y) with all terms in {0,...,n} and w = min(|w-x|, |x-y|, |y-w|).

%I A213495 #21 Feb 19 2024 11:42:40
%S A213495 1,4,9,16,27,38,53,70,89,110,135,160,189,220,253,288,327,366,409,454,
%T A213495 501,550,603,656,713,772,833,896,963,1030,1101,1174,1249,1326,1407,
%U A213495 1488,1573,1660,1749,1840,1935,2030,2129,2230,2333,2438,2547,2656
%N A213495 Number of (w,x,y) with all terms in {0,...,n} and w = min(|w-x|, |x-y|, |y-w|).
%C A213495 For a guide to related sequences, see A212959.
%H A213495 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,-1,-1,1).
%F A213495 a(n) = a(n-1) + a(n-2) - a(n-4) - a(n-5) + a(n-6).
%F A213495 G.f.: (1 + 3*x + 4*x^2 + 3*x^3 + 3*x^4)/(1 - x - x^2 + x^4 + x^5 - x^6).
%F A213495 a(n) = (n+1)^3 - A213492(n).
%t A213495 t = Compile[{{n, _Integer}}, Module[{s = 0}, (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 A213495 m = Map[t[#] &, Range[0, 60]]
%t A213495 (* or *)
%t A213495 LinearRecurrence[{1, 1, 0, -1, -1, 1}, {1, 4, 9, 16, 27, 38}, 60]
%t A213495 CoefficientList[Series[(1+3x+4x^2+3x^3+3x^4)/(1-x-x^2+x^4+x^5-x^6),{x,0,50}],x] (* _Harvey P. Dale_, Aug 11 2021 *)
%Y A213495 Cf. A212959, A213492.
%K A213495 nonn,easy
%O A213495 0,2
%A A213495 _Clark Kimberling_, Jun 13 2012