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 A159287 #44 Nov 18 2024 02:54:11
%S A159287 0,0,1,0,1,2,1,4,5,6,13,16,25,42,57,92,141,206,325,488,737,1138,1713,
%T A159287 2612,3989,6038,9213,14016,21289,32442,49321,75020,114205,173662,
%U A159287 264245,402072,611569,930562,1415713,2153700,3276837,4985126,7584237,11538800
%N A159287 Expansion of x^2/(1-x^2-2*x^3).
%C A159287 A floretion-generated sequence: 'i + 0.5('ij' + 'ik' + 'ji' + 'jk' + 'ki' + 'kj').
%C A159287 From _Greg Dresden_, Nov 15 2024: (Start)
%C A159287 a(n) is the number of ways to tile a 2 X (n+1) board with L-shaped trominos and S-shaped quadrominos, where the first tile must be an upright L. For example, here are the a(7)=4 ways to tile a 2 X 8 board:
%C A159287 ._______________. ._______________.
%C A159287 | |_ | _| _| | | |_ |_ | _| |
%C A159287 |___|_|_|___|___| |___|___|_|_|___|
%C A159287 ._______________. ._______________.
%C A159287 | |_ | |_ |_ | | |_ |_ | |_ |
%C A159287 |___|_|___|___|_| |___|___|_|___|_| (End)
%H A159287 G. C. Greubel, <a href="/A159287/b159287.txt">Table of n, a(n) for n = 0..1000</a>
%H A159287 Creighton Dement, <a href="https://web.archive.org/web/20211129085739/http://fumba.eu/sitelayout/Floretion.php">Online Floretion Multiplier</a>.
%H A159287 Yüksel Soykan, <a href="https://doi.org/10.34198/ejms.4220.227251">A Study on Generalized Jacobsthal-Padovan Numbers</a>, Earthline Journal of Mathematical Sciences (2020) Vol. 4, No. 2, 227-251.
%H A159287 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,2).
%F A159287 G.f.: x^2/(1-x^2-2*x^3).
%F A159287 a(n) = A052947(n-2). - _R. J. Mathar_, Nov 10 2009
%F A159287 a(n) = a(n-2) + 2*a(n-3). - _Wesley Ivan Hurt_, May 23 2023
%F A159287 From _Greg Dresden_, Nov 17 2024: (Start)
%F A159287 a(2*n+1) = 2*a(n)^2 + 2*a(n+1)*a(n+2).
%F A159287 a(3*n+1) = Sum_{i=1..n} a(3*i-2)*2^(n-i). (End)
%t A159287 LinearRecurrence[{0, 1, 2}, {0, 0, 1}, 60] (* _Vladimir Joseph Stephan Orlovsky_, May 24 2011 *)
%t A159287 CoefficientList[Series[x^2/(1-x^2-2x^3),{x,0,50}],x] (* _Harvey P. Dale_, May 29 2021 *)
%o A159287 (PARI) a(n)=([0,1,0; 0,0,1; 2,1,0]^n*[0;0;1])[1,1] \\ _Charles R Greathouse IV_, Oct 03 2016
%o A159287 (Magma) I:=[0,0,1]; [n le 3 select I[n] else Self(n-2) + 2*Self(n-3): n in [1..30]]; // _G. C. Greubel_, Jun 27 2018
%Y A159287 Cf. A159284, A159285, A159286, A159288.
%Y A159287 Essentially the same as A052947.
%K A159287 easy,nonn
%O A159287 0,6
%A A159287 _Creighton Dement_, Apr 08 2009