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A022121 Fibonacci sequence beginning 3, 8. 7
3, 8, 11, 19, 30, 49, 79, 128, 207, 335, 542, 877, 1419, 2296, 3715, 6011, 9726, 15737, 25463, 41200, 66663, 107863, 174526, 282389, 456915, 739304, 1196219, 1935523, 3131742, 5067265, 8199007, 13266272, 21465279, 34731551, 56196830, 90928381, 147125211 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
From Wajdi Maaloul, Jun 20 2022: (Start)
a(n) is the number of ways to tile the figure below with squares and dominoes (a strip of length n+2 that contains two vertical strip of height 2 in its first and third tiles).
_ _
|_|_|_|_____ _
|_|_|_|_|_|_|...|_|
(End)
LINKS
Tanya Khovanova, Recursive Sequences
FORMULA
G.f.: (3+5*x)/(1-x-x^2). - Philippe Deléham, Nov 19 2008
a(n) = F(n+2) + 2*L(n+1), where F(n) and L(n) are the n-th Fibonacci and Lucas number, respectively. - Rigoberto Florez, Jan 29 2020
E.g.f.: exp(-2*x/(1+sqrt(5)))*(-2*(5+6*sqrt(5))+(55+27*sqrt(5))*exp(sqrt(5)*x))/(5*(3+sqrt(5))). - Stefano Spezia, Jan 29 2020 after Rigoberto Florez
a(n) = Lucas(n+3) + Fibonacci(n-2). - Greg Dresden and Steve Warren, Feb 28 2022
MATHEMATICA
LinearRecurrence[{1, 1}, {3, 8}, 40] (* Vladimir Joseph Stephan Orlovsky, Sep 17 2008 *)
Table[2 LucasL[n+1] + Fibonacci[n+2], {n, 0, 40}] (* Rigoberto Florez, Jan 29 2020 *)
PROG
(Magma) a0:=3; a1:=8; [GeneralizedFibonacciNumber(a0, a1, n): n in [0..40]]; // Vincenzo Librandi, Jan 25 2017
(PARI) apply( {A022121(n)=[3, 8]*([0, 1; 1, 1]^n)[, 1]}, [0..30]) \\ M. F. Hasler, Feb 28 2020
CROSSREFS
Sequence in context: A105410 A114548 A182759 * A364086 A171672 A341262
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified June 14 20:28 EDT 2024. Contains 373401 sequences. (Running on oeis4.)