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

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A099843 A transform of the Fibonacci numbers. 1
1, -5, 21, -89, 377, -1597, 6765, -28657, 121393, -514229, 2178309, -9227465, 39088169, -165580141, 701408733, -2971215073, 12586269025, -53316291173, 225851433717, -956722026041, 4052739537881, -17167680177565, 72723460248141, -308061521170129, 1304969544928657 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The g.f. is the transform of the g.f. of A000045 under the mapping G(x)-> (-1/(1+x))G((x-1)/(x+1)). In general this mapping transforms x/(1-kx-kx^2) into (1-x)/(1+2(k+1)x-(2k-1)x^2).

Pisano period lengths: 1, 1, 8, 2, 20, 8, 16, 4, 8, 20, 10, 8, 28, 16, 40, 8, 12, 8, 6, 20, ... - R. J. Mathar, Aug 10 2012

LINKS

Table of n, a(n) for n=0..24.

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (-4,1)

FORMULA

G.f.: (1-x)/(1+4x-x^2); a(n) = (sqrt(5)-2)^n(1/2-3*sqrt(5)/10)+(-sqrt(5)-2)^n(1/2+3*sqrt(5)/10); a(n) = (-1)^n*Fibonacci(3n+2).

a(n) = -4*a(n-1)+a(n-2), a(0)=1, a(1)=-5. - Philippe Deléham, Nov 03 2008

a(n) = (-1)^n*(A001076(n)+A001076(n+1)). - R. J. Mathar, Aug 10 2012

MATHEMATICA

CoefficientList[Series[(x - 1)/(x^2 - 4 x - 1), {x, 0, 30}], x] (* Vladimir Joseph Stephan Orlovsky, Jun 10 2011 *)

LinearRecurrence[{-4, 1}, {1, -5}, 30] (* Harvey P. Dale, Aug 13 2015 *)

CROSSREFS

Cf. A099842, A015448, A152174 (binomial transform), A084326 (shifted unsigned inverse binomial transform).

Sequence in context: A273643 A240461 A273860 * A015448 A273796 A035011

Adjacent sequences:  A099840 A099841 A099842 * A099844 A099845 A099846

KEYWORD

easy,sign

AUTHOR

Paul Barry, Oct 27 2004

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 November 21 12:34 EST 2017. Contains 295001 sequences.