A022124 Fibonacci sequence beginning 3, 13.

3, 13, 16, 29, 45, 74, 119, 193, 312, 505, 817, 1322, 2139, 3461, 5600, 9061, 14661, 23722, 38383, 62105, 100488, 162593, 263081, 425674, 688755, 1114429, 1803184, 2917613, 4720797, 7638410, 12359207

Offset

0,1

Comments

For n >= 5, 4*a(n) is the number of ways to tile, with squares and dominoes, a horizontal strip of length n+1 that begins and ends with two vertical strips of heights 3 and 2. As an example, 4*a(7) = 4*193 = 772 is the number of ways to tile this figure (of length 8) with squares and dominoes.

._ _

|_|_ _|_|

|_|_|_______|_|_|

|_|_|_|_|_|_|_|_| - Reeva Bohra and Greg Dresden, Aug 17 2021

Links

Harvey P. Dale, 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.: (3+10x)/(1-x-x^2). - Philippe Deléham, Nov 19 2008

a(n) = 5*Lucas(n+1) - 2*Fibonacci(n+1). - Lechoslaw Ratajczak, Apr 04 2021

Mathematica

LinearRecurrence[{1, 1}, {3, 13}, 40] (* Harvey P. Dale, Jun 08 2016 *)

Crossrefs

Cf. A000032, A000045, A022382.

Sequence in context: A152269 A063674 A273678 * A042133 A041297 A041815

Adjacent sequences: A022121 A022122 A022123 * A022125 A022126 A022127

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved