This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A020992 #54 Jul 03 2025 01:14:32
%S A020992 0,2,1,3,6,10,19,35,64,118,217,399,734,1350,2483,4567,8400,15450,
%T A020992 28417,52267,96134,176818,325219,598171,1100208,2023598,3721977,
%U A020992 6845783,12591358,23159118,42596259,78346735,144102112,265045106,487493953,896641171,1649180230
%N A020992 a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 0, a(1) = 2, a(2) = 1.
%C A020992 Tribonacci sequence beginning 0, 2, 1.
%C A020992 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 A020992 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
%C A020992 From _Greg Dresden_ and Jiarui Zhou, Jun 30 2025: (Start)
%C A020992 For n >= 4, 2*a(n) is the number of ways to tile this shape of length n-2 with squares, dominos, and trominos (of length 3):
%C A020992 .___
%C A020992 |_|_|___________
%C A020992 |_|_|_|_|_|_|_|_|
%C A020992 |_|.
%C A020992 As an example, here is one of the 2*a(10) = 434 ways to tile this shape of length 8:
%C A020992 .___
%C A020992 | |_|___________
%C A020992 | |___|_____|_|_|
%C A020992 |_| (End)
%H A020992 Robert Price, <a href="/A020992/b020992.txt">Table of n, a(n) for n = 0..1000</a>
%H A020992 Martin Burtscher, Igor Szczyrba, and Rafał 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 A020992 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1).
%F A020992 G.f.: x*(2-x)/(1-x-x^2-x^3).
%F A020992 a(n) = 2*A000073(n+1)-A000073(n). - _R. J. Mathar_, Aug 22 2008
%F A020992 a(n) = 2*a(n-1) - a(n-4), n>3. - _Vincenzo Librandi_, Jun 08 2011
%t A020992 LinearRecurrence[{1,1,1},{0,2,1},100] (* _Vladimir Joseph Stephan Orlovsky_, Jun 07 2011 *)
%o A020992 (PARI) my(x='x+O('x^30)); concat([0], Vec(x*(2-x)/(1-x-x^2-x^3))) \\ _G. C. Greubel_, Feb 09 2018
%o A020992 (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 A020992 Cf. A000032, A000073, A001590, A232498, A233554.
%K A020992 nonn,easy
%O A020992 0,2
%A A020992 _N. J. A. Sloane_