login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A117591 2^n + Fibonacci(n). 7
1, 3, 5, 10, 19, 37, 72, 141, 277, 546, 1079, 2137, 4240, 8425, 16761, 33378, 66523, 132669, 264728, 528469, 1055341, 2108098, 4212015, 8417265, 16823584, 33629457, 67230257, 134414146, 268753267, 537385141, 1074573864, 2148829917 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(3n) is even if n>0. - Robert G. Wilson v, Sep 06 2002

3 divides a(8n+1) and a(8n-1). - Enrique Pérez Herrero, Dec 29 2010

a(n) = A000079(n+1) - A099036(n) = A099036(n) + 2 * A000045(n). - Reinhard Zumkeller, Aug 15 2013

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-1,-2).

FORMULA

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

MATHEMATICA

Table[f=Fibonacci[n]; 2^n+f, {n, 1, 40, 1}] (* Vladimir Joseph Stephan Orlovsky, Jul 23 2008 *)

CoefficientList[Series[(1 - 3 x^2)/((1 - x - x^2) (1 - 2 x)), {x, 0, 35}], x] (* Vincenzo Librandi, Nov 02 2014 *)

PROG

(Haskell)

a117591 n = a117591_list !! n

a117591_list = zipWith (+) a000079_list a000045_list

-- Reinhard Zumkeller, Aug 15 2013

(MAGMA) [2^n+Fibonacci(n): n in [0..40]]; // Vincenzo Librandi, Nov 02 2014

(PARI) a(n)=2^n + fibonacci(n) \\ Charles R Greathouse IV, Oct 07 2016

CROSSREFS

Cf. A000045, A000079, A074824, A001611, A212262.

Sequence in context: A133999 A238431 A014610 * A003055 A217925 A018101

Adjacent sequences:  A117588 A117589 A117590 * A117592 A117593 A117594

KEYWORD

nonn,easy

AUTHOR

Franklin T. Adams-Watters, Apr 04 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 6 06:58 EST 2016. Contains 278775 sequences.