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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

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Last modified March 25 11:34 EDT 2017. Contains 284076 sequences.