OFFSET
0,1
COMMENTS
From Wajdi Maaloul, Jun 19 2022: (Start)
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.
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(End)
From Greg Dresden, Jun 26 2022: (Start)
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.
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(End)
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (1,1).
FORMULA
G.f.: (5+6*x)/(1-x-x^2). - Philippe Deléham, Nov 20 2008
a(n) = 2*Lucas(n-1) + 7*Fibonacci(n+1). - Lechoslaw Ratajczak, May 01 2017
a(n) = Fibonacci(n+6) - Fibonacci(n+1) - Lucas(n). - Greg Dresden and Aamen Muharram, Jul 22 2022
MATHEMATICA
Transpose[NestList[{Last[#], Total[#]}&, {5, 11}, 40]][[1]] (* Harvey P. Dale, Apr 04 2011 *)
LinearRecurrence[{1, 1}, {5, 11}, 40] (* Vincenzo Librandi, May 03 2017 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved