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 A022136 #53 Jun 28 2025 12:25:23
%S A022136 5,11,16,27,43,70,113,183,296,479,775,1254,2029,3283,5312,8595,13907,
%T A022136 22502,36409,58911,95320,154231,249551,403782,653333,1057115,1710448,
%U A022136 2767563,4478011,7245574,11723585,18969159,30692744,49661903,80354647,130016550
%N A022136 Fibonacci sequence beginning 5, 11.
%C A022136 From _Wajdi Maaloul_, Jun 19 2022: (Start)
%C A022136 For n > 0, 2*a(n) is the number of ways to tile this strip of length n+1 (beginning with two vertical strips of length 3) using squares and dominoes.
%C A022136 ._ _
%C A022136 |_|_|
%C A022136 |_|_|_______________ _
%C A022136 |_|_|_|_|_|_|_|_|_|_|...|_|
%C A022136 (End)
%C A022136 From _Greg Dresden_, Jun 26 2022: (Start)
%C A022136 For n > 0, 5*a(n) is the number of ways to tile this strip of length n (beginning with a long vertical strip of length 9) using squares and dominoes.
%C A022136 ._
%C A022136 |_|
%C A022136 |_|
%C A022136 |_|
%C A022136 |_|_________________ _
%C A022136 |_|_|_|_|_|_|_|_|_|_|...|_|
%C A022136 |_|
%C A022136 |_|
%C A022136 |_|
%C A022136 |_|
%C A022136 (End)
%C A022136 The 5-adic evaluation of this sequence is A112765(a(n)) = 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2,.. and has records of nu_5 = 1, 2, 3, 4, 5, 7, 8,... at n=0, 10, 85, 585, 3085, 12460, 168710,... Does this grow without bounds? [StackExchange] - _R. J. Mathar_, Jun 28 2025
%H A022136 Vincenzo Librandi, <a href="/A022136/b022136.txt">Table of n, a(n) for n = 0..1000</a>
%H A022136 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A022136 StackExchange, <a href="https://math.stackexchange.com/questions/5078975">nu_5(5F_(n+2)+F_n)</a>, Jun 2025.
%H A022136 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,1).
%F A022136 G.f.: (5+6*x)/(1-x-x^2). - _Philippe Deléham_, Nov 20 2008
%F A022136 a(n) = 2*Lucas(n-1) + 7*Fibonacci(n+1). - _Lechoslaw Ratajczak_, May 01 2017
%F A022136 a(n) = Fibonacci(n+6) - Fibonacci(n+1) - Lucas(n). - _Greg Dresden_ and _Aamen Muharram_, Jul 22 2022
%t A022136 Transpose[NestList[{Last[#],Total[#]}&,{5,11},40]][[1]] (* _Harvey P. Dale_, Apr 04 2011 *)
%t A022136 LinearRecurrence[{1, 1}, {5, 11}, 40] (* _Vincenzo Librandi_, May 03 2017 *)
%Y A022136 Cf. A000032, A000045.
%K A022136 nonn,easy
%O A022136 0,1
%A A022136 _N. J. A. Sloane_