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
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved