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A022124
Fibonacci sequence beginning 3, 13.
2
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.
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|_|_|_|_|_|_|_|_| - Reeva Bohra and Greg Dresden, Aug 17 2021
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
KEYWORD
nonn,easy
STATUS
approved