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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 Vincenzo Librandi, 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+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 Cf. A000032, A000045. Sequence in context: A105410 A114548 A182759 * A364086 A171672 A341262 Adjacent sequences: A022118 A022119 A022120 * A022122 A022123 A022124 KEYWORD nonn,easy AUTHOR N. J. A. Sloane STATUS approved

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