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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A106568 Expansion of 4*x/(1-4*x-4*x^2). 0
0, 4, 16, 80, 384, 1856, 8960, 43264, 208896, 1008640, 4870144, 23515136, 113541120, 548225024, 2647064576, 12781158400, 61712891904, 297976201216, 1438756372480, 6946930294784, 33542746669056, 161958707855360 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Previous name was: First entry of the vector (M^n)v, where M is the 2 X 2 matrix [[0,4],[1,4]] and v is the column vector [0,1].

LINKS

Table of n, a(n) for n=0..21.

Martin Burtscher, Igor Szczyrba, Rafał Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.

Tanya Khovanova, Recursive Sequences

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

FORMULA

a(n) = 4 * A057087(n).

a(n) = A094013(n+1). - R. J. Mathar, Aug 24 2008

From Philippe Deléham, Sep 19 2009: (Start)

a(n) = 4*a(n-1) + 4*a(n-2) for n > 2; a(0) = 0, a(1)=4.

G.f.: 4x/(1-4x-4x^2). (End)

G.f.: Q(0) - 1, where Q(k) = 1 + 2*(1+2*x)*x + 2*(2*k+3)*x - 2*x*(2*k+1 +2*x+1)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Oct 04 2013

MAPLE

with(linalg): M:=matrix(2, 2, [0, 4, 1, 4]): v[0]:=matrix(2, 1, [0, 1]): for n from 1 to 23 do v[n]:=multiply(M, v[n-1]) od: seq(v[n][1, 1], n=0..23);

MATHEMATICA

M = {{0, 4}, {1, 4}} v[1] = {0, 1} v[n_] := v[n] = M.v[n - 1] a = Table[v[n][[1]], {n, 1, 50}]

CROSSREFS

Cf. A009013.

Sequence in context: A081682 A068788 A094013 * A183146 A160564 A075581

Adjacent sequences:  A106565 A106566 A106567 * A106569 A106570 A106571

KEYWORD

nonn,easy,less

AUTHOR

Roger L. Bagula, May 30 2005

EXTENSIONS

Edited by N. J. A. Sloane, Apr 30 2006

Simpler name using o.g.f. by Joerg Arndt, Oct 05 2013

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 November 30 04:01 EST 2020. Contains 338781 sequences. (Running on oeis4.)