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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A099843 A transform of the Fibonacci numbers. 1

%I

%S 1,-5,21,-89,377,-1597,6765,-28657,121393,-514229,2178309,-9227465,

%T 39088169,-165580141,701408733,-2971215073,12586269025,-53316291173,

%U 225851433717,-956722026041,4052739537881,-17167680177565,72723460248141,-308061521170129,1304969544928657

%N A transform of the Fibonacci numbers.

%C 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).

%C 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

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-4,1)

%F 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).

%F a(n) = -4*a(n-1)+a(n-2), a(0)=1, a(1)=-5. - _Philippe Deléham_, Nov 03 2008

%F a(n) = (-1)^n*(A001076(n)+A001076(n+1)). - _R. J. Mathar_, Aug 10 2012

%F a(n) = (-1)^n*A015448(n+1). - _R. J. Mathar_, May 07 2019

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

%t LinearRecurrence[{-4,1},{1,-5},30] (* _Harvey P. Dale_, Aug 13 2015 *)

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

%K easy,sign

%O 0,2

%A _Paul Barry_, Oct 27 2004

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 November 21 11:35 EST 2019. Contains 329370 sequences. (Running on oeis4.)