A190995 Fibonacci sequence beginning 9, 7.

9, 7, 16, 23, 39, 62, 101, 163, 264, 427, 691, 1118, 1809, 2927, 4736, 7663, 12399, 20062, 32461, 52523, 84984, 137507, 222491, 359998, 582489, 942487, 1524976, 2467463, 3992439, 6459902, 10452341, 16912243, 27364584, 44276827, 71641411, 115918238, 187559649

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

Cf. A000032, A000045, A190994.

Sequence in context: A011405 A268228 A131724 * A186830 A124050 A107663

Adjacent sequences: A190992 A190993 A190994 * A190996 A190997 A190998

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Jun 07 2011

Status

approved