OFFSET
0,1
COMMENTS
From Wajdi Maaloul, Jun 20 2022: (Start)
For n>0, 2*a(n) is the number of ways to tile this figure below with squares and dominoes (a strip of length n+1 that begins with a length 3 vertical strip and length 4 one).
_
_|_|
|_|_|
|_|_|_______ _
|_|_|_|_|_|_|...|_|
(End)
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1).
FORMULA
a(n) = ((9+sqrt(5))/2)*((1+sqrt(5))/2)^n + ((9-sqrt(5))/2)*((1-sqrt(5))/2)^n. - Antonio Alberto Olivares
G.f.: (9-2*x)/(1-x-x^2). - Colin Barker, Jan 11 2012
a(n) = 7*Fibonacci(n) + 9*Fibonacci(n-1) = 7*Fibonacci(n+1) + 2*Fibonacci(n-1) = 7*Lucas(n) - 5*Fibonacci(n-1) for n>0. - Wajdi Maaloul, Jun 20 2022
MAPLE
a:= n-> (<<0|1>, <1|1>>^n. <<9, 7>>)[1, 1]:
seq(a(n), n=0..36); # Alois P. Heinz, Oct 26 2022
MATHEMATICA
LinearRecurrence[{1, 1}, {9, 7}, 100]
PROG
(PARI) a(n)=7*fibonacci(n)+9*fibonacci(n-1) \\ Charles R Greathouse IV, Jun 08 2011
(Magma) [n le 2 select 11-2*n else Self(n-1)+Self(n-2): n in [1..50]]; \\ Vincenzo Librandi, Feb 15 2012
(SageMath) [7*fibonacci(n) + 9*fibonacci(n-1) for n in range(51)] # G. C. Greubel, Oct 26 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vladimir Joseph Stephan Orlovsky, Jun 07 2011
STATUS
approved