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
A. Muhammed Uludağ and Buket Eren Gökmen, The conumerator and the codenominator, Bulletin des Sciences Mathématiques, Volume 180, November 2022, 103192.
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
a(n) = 3*fibonacci(n+1) + 2*fibonacci(n-1). See Uludağ link. - Michel Marcus, Jul 24 2026
MATHEMATICA
LinearRecurrence[{1, 1}, {3, 8}, 40] (* Vladimir Joseph Stephan Orlovsky, Sep 17 2008 *)
(* Alternative: *)
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved