A022136 Fibonacci sequence beginning 5, 11.

5, 11, 16, 27, 43, 70, 113, 183, 296, 479, 775, 1254, 2029, 3283, 5312, 8595, 13907, 22502, 36409, 58911, 95320, 154231, 249551, 403782, 653333, 1057115, 1710448, 2767563, 4478011, 7245574, 11723585, 18969159, 30692744, 49661903, 80354647, 130016550

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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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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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

Cf. A000032, A000045.

Sequence in context: A314181 A314182 A035108 * A042385 A041046 A041117

Adjacent sequences: A022133 A022134 A022135 * A022137 A022138 A022139

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved