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%I #12 Dec 04 2016 19:46:27
%S 0,6,24,60,114,186,276,384,510,654,816,996,1194,1410,1644,1896,2166,
%T 2454,2760,3084,3426,3786,4164,4560,4974,5406,5856,6324,6810,7314,
%U 7836,8376,8934,9510,10104,10716,11346,11994,12660,13344,14046
%N Number of ordered triples (w,x,y) with all terms in {-n,...-1,1,...,n} and -1<=w+x+y<=1.
%C For a guide to related sequences, see A211422.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 1).
%F a(n)= 6*A005448(n).
%F a(n) = 3a(n-1)-3a(n-2)+a(n-3) for n>3.
%F a(n) = 6-9*n+9*n^2 for n>0. G.f.: 6*x*(1+x+x^2)/(1-x)^3. [_Colin Barker_, Sep 09 2012]
%t t = Compile[{{u, _Integer}}, Module[{s = 0}, (Do[If[-1 <= w + x + y <= 1, s = s + 1], {w, #}, {x, #}, {y, #}] &[Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]];
%t Map[t[#] &, Range[0, 70]] (* A211615 *)
%t %/6 (* A005448 *)
%t FindLinearRecurrence[%]
%t (* _Peter J. C. Moses_, Apr 13 2012 *)
%t Join[{0},LinearRecurrence[{3, -3, 1},{6, 24, 60},40]] (* _Ray Chandler_, Aug 02 2015 *)
%Y Cf. A211422.
%K nonn,easy
%O 0,2
%A _Clark Kimberling_, Apr 16 2012
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