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%I #50 Jul 24 2022 13:34:48
%S 5,11,16,27,43,70,113,183,296,479,775,1254,2029,3283,5312,8595,13907,
%T 22502,36409,58911,95320,154231,249551,403782,653333,1057115,1710448,
%U 2767563,4478011,7245574,11723585,18969159,30692744,49661903,80354647,130016550
%N Fibonacci sequence beginning 5, 11.
%C From _Wajdi Maaloul_, Jun 19 2022: (Start)
%C 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 ._ _
%C |_|_|
%C |_|_|_______________ _
%C |_|_|_|_|_|_|_|_|_|_|...|_|
%C (End)
%C From _Greg Dresden_, Jun 26 2022: (Start)
%C 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 ._
%C |_|
%C |_|
%C |_|
%C |_|_________________ _
%C |_|_|_|_|_|_|_|_|_|_|...|_|
%C |_|
%C |_|
%C |_|
%C |_|
%C (End)
%H Vincenzo Librandi, <a href="/A022136/b022136.txt">Table of n, a(n) for n = 0..1000</a>
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,1).
%F G.f.: (5+6*x)/(1-x-x^2). - _Philippe Deléham_, Nov 20 2008
%F a(n) = 2*Lucas(n-1) + 7*Fibonacci(n+1). - _Lechoslaw Ratajczak_, May 01 2017
%F a(n) = Fibonacci(n+6) - Fibonacci(n+1) - Lucas(n). - _Greg Dresden_ and _Aamen Muharram_, Jul 22 2022
%t Transpose[NestList[{Last[#],Total[#]}&,{5,11},40]][[1]] (* _Harvey P. Dale_, Apr 04 2011 *)
%t LinearRecurrence[{1, 1}, {5, 11}, 40] (* _Vincenzo Librandi_, May 03 2017 *)
%Y Cf. A000032, A000045.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
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