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%I M2351 #48 Sep 08 2022 08:44:35
%S 1,3,4,8,15,27,50,92,169,311,572,1052,1935,3559,6546,12040,22145,
%T 40731,74916,137792,253439,466147,857378,1576964,2900489,5334831,
%U 9812284,18047604,33194719,61054607,112296930,206546256,379897793,698740979,1285185028
%N a(n) = a(n-1) + a(n-2) + a(n-3).
%C If A001590 is the tribonacci sequence, this might be called the Trucas sequence after the Lucas sequence A000032. - Paul Wayper (paulway(AT)mabula.net), Nov 28 2007
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence)
%H Vincenzo Librandi, <a href="/A007486/b007486.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.html">Analytic Representations of the n-anacci Constants and Generalizations Thereof</a>, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.
%H N. G. Voll, <a href="https://www.fq.math.ca/Papers1/51-3/Voll4-TermRecurrence.pdf">Some identities for four term recurrence relations</a>, Fib. Quart., 51 (2013), 268-273.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1).
%F O.g.f.: x*(1+2*x)/(1-x-x^2-x^3). a(n) = A001590(n)+3*A000073(n). - _R. J. Mathar_, Aug 22 2008
%F a(n) = 2*a(n-1) - a(n-4), n>4. - _Vincenzo Librandi_, Jun 08 2011
%t LinearRecurrence[{1,1,1},{1,3,4},100] (* _Vladimir Joseph Stephan Orlovsky_, Jun 07 2011 *)
%t CoefficientList[Series[(1 + 2 x) / (1 - x - x^2 - x^3), {x, 0, 40}], x] (* _Vincenzo Librandi_, Jun 09 2013 *)
%o (PARI) Vec((x+2*x^2)/(1-x-x^2-x^3)+O(x^99)) \\ _Charles R Greathouse IV_, Jun 08 2011
%o (Magma) I:=[1,3,4]; [n le 3 select I[n] else Self(n-1)+Self(n-2)+Self(n-3): n in [1..50]]; // _Vincenzo Librandi_, Jun 09 2013
%Y Cf. A001590, A000032, A000045.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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