login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A122069 a(n) = 3*a(n-1) + 9*a(n-2) for n > 1, with a(0)=1, a(1)=3. 3
1, 3, 18, 81, 405, 1944, 9477, 45927, 223074, 1082565, 5255361, 25509168, 123825753, 601059771, 2917611090, 14162371209, 68745613437, 333698181192, 1619805064509, 7862698824255, 38166342053346, 185263315578333 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,9).

FORMULA

a(n) = 3^n*Fibonacci(n+1) = 3^n*A000045(n+1).

a(n) = Sum_{k=0..n} 2^k*A016095(n,k).

G.f.: 1/(1-3*x-9*x^2).

a(n+1)/a(n) -> 3*((1+sqrt(5))/2 if n ->infinity.

a(n) = A099012(n+1). - R. J. Mathar, Aug 02 2008

a(n) = (1/2)*((3/2)+(3/2)*sqrt(5))^n+(1/10)*((3/2)+(3/2)*sqrt(5))^n*sqrt(5)-(1/10)*sqrt(5)*((3/2)-(3/2)*sqrt(5))^n+(1/2)*((3/2)-(3/2)*sqrt(5))^n, with n >= 0. - Paolo P. Lava, Nov 19 2008

a(n) = A085504(n) for n >= 2. - Georg Fischer, Nov 03 2018

MAPLE

with(combinat); seq(3^n*fibonacci(n+1), n=0..25); # G. C. Greubel, Oct 03 2019

MATHEMATICA

Table[3^n*Fibonacci[n+1], {n, 0, 25}] (* G. C. Greubel, Oct 03 2019 *)

LinearRecurrence[{3, 9}, {1, 3}, 30] (* Harvey P. Dale, Apr 28 2020 *)

PROG

(Sage) [lucas_number1(n, 3, -9) for n in range(1, 23)] # Zerinvary Lajos, Apr 22 2009

(PARI) vector(26, n, 3^(n-1)*fibonacci(n) ) \\ G. C. Greubel, Oct 03 2019

(MAGMA) [3^n*Fibonacci(n+1): n in [0..25]]; // G. C. Greubel, Oct 03 2019

(GAP) List([0..25], n-> 3^n*Fibonacci(n+1) ); # G. C. Greubel, Oct 03 2019

CROSSREFS

Third row of A234357.

Cf. A000045, A085504, A099012.

Sequence in context: A036290 A078904 A099012 * A103897 A119424 A301996

Adjacent sequences:  A122066 A122067 A122068 * A122070 A122071 A122072

KEYWORD

nonn,easy

AUTHOR

Philippe Deléham, Oct 15 2006

EXTENSIONS

Corrected by T. D. Noe, Nov 07 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 26 13:34 EDT 2021. Contains 347668 sequences. (Running on oeis4.)