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%I #14 Sep 08 2022 08:45:38
%S 2,3,4,9,16,29,54,99,182,335,616,1133,2084,3833,7050,12967,23850,
%T 43867,80684,148401,272952,502037,923390,1698379,3123806,5745575,
%U 10567760,19437141,35750476,65755377,120942994,222448847,409147218
%N a(n) = a(n-1) + a(n-2) + a(n-3) with a(1) = 2, a(2) = 3, a(3) = 4.
%C If the conjectured recurrence in A000382 is correct, then a(n) = A000382(n+2) - A000382(n+1), n>=4. - _R. J. Mathar_, Jan 30 2011
%H G. C. Greubel, <a href="/A145027/b145027.txt">Table of n, a(n) for n = 1..1000</a>
%H Martin Burtscher, Igor Szczyrba, Rafał Szczyrba, <a href="http://www.emis.de/journals/JIS/VOL18/Szczyrba/sz3.pdf">Analytic Representations of the n-anacci Constants and Generalizations Thereof</a>, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1).
%F From _R. J. Mathar_, Jan 30 2011: (Start)
%F a(n) = -A000073(n-1) + A000073(n) + 2*A000073(n+1).
%F G.f. x*(1+x)*(2-x)/(1-x-x^2-x^3). (End)
%t LinearRecurrence[{1,1,1},{2,3,4},33] (* _Ray Chandler_, Dec 08 2013 *)
%o (PARI) my(x='x+O('x^30)); Vec(x*(1+x)*(2-x)/(1-x-x^2-x^3)) \\ _G. C. Greubel_, Apr 22 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( x*(1+x)*(2-x)/(1-x-x^2-x^3) )); // _G. C. Greubel_, Apr 22 2019
%o (Sage) a=(x*(1+x)*(2-x)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False); a[1:] # _G. C. Greubel_, Apr 22 2019
%Y Cf. A000073, A000213, A001590, A003265, A056816, A081172, A001644.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Sep 30 2008
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