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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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.

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|||_|||_||| - 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).

Crossrefs

Cf. A000032, A000045, A022382.

Programs

Mathematica

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

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