%I #41 Sep 08 2022 08:44:45
%S 0,2,1,3,6,10,19,35,64,118,217,399,734,1350,2483,4567,8400,15450,
%T 28417,52267,96134,176818,325219,598171,1100208,2023598,3721977,
%U 6845783,12591358,23159118,42596259,78346735,144102112,265045106,487493953,896641171,1649180230
%N a(n) = a(n-1) + a(n-2) + a(n-3).
%C Tribonacci sequence beginning 0, 2, 1.
%C Pisano period lengths: 1, 4, 13, 8, 31, 52, 48, 16, 39, 124, 110, 104, 168, 48, 403, 32, 96, 156, 360, 248,.... - _R. J. Mathar_, Aug 10 2012
%C One bisection is 0, 1, 6, 19, 64, 217, 734, 2483, 8400,.. and the other 2, 3, 10, 35, 118, 399, 1350, 4567,... both with recurrence b(n)=3*b(n-1)+b(n-2)+b(n-3). - _R. J. Mathar_, Aug 10 2012
%H Robert Price, <a href="/A020992/b020992.txt">Table of n, a(n) for n = 0..1000</a>
%H Martin Burtscher, Igor Szczyrba, RafaĆ Szczyrba, <a href="https://www.emis.de/journals/JIS/VOL18/Szczyrba/sz3.html">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 G.f.: x*(2-x)/(1-x-x^2-x^3).
%F a(n) = 2*A000073(n+1)-A000073(n). - _R. J. Mathar_, Aug 22 2008
%F a(n) = 2*a(n-1) - a(n-4), n>3. - _Vincenzo Librandi_, Jun 08 2011
%t LinearRecurrence[{1,1,1},{0,2,1},100] (* _Vladimir Joseph Stephan Orlovsky_, Jun 07 2011 *)
%o (PARI) x='x+O('x^30); concat([0], Vec(x*(2-x)/(1-x-x^2-x^3))) \\ _G. C. Greubel_, Feb 09 2018
%o (Magma) I:=[0,2,1]; [n le 3 select I[n] else Self(n-1) + Self(n-2) + Self(n-3): n in [1..30]]; // _G. C. Greubel_, Feb 09 2018
%Y Cf. A000032, A000073, A001590, A232498, A233554.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_