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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A089772 Lucas numbers L(11n). 2
2, 199, 39603, 7881196, 1568397607, 312119004989, 62113250390418, 12360848946698171, 2459871053643326447, 489526700523968661124, 97418273275323406890123, 19386725908489881939795601, 3858055874062761829426214722 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n+1)/a(n) converges to (199+sqrt(39605))/2 = 199.00502499874... a(0)/a(1)=2/199; a(1)/a(2)=199/39603; a(2)/a(3)= 39603/7881196; a(3)/a(4)= 7881196/1568397607; ... etc. Lim a(n)/a(n+1) as n approaches infinity = 0.00502499874... = 2/(199+sqrt(39605)) = (sqrt(39605)-199)/2.

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 0..100

Tanya Khovanova, Recursive Sequences

Index entries for recurrences a(n) = k*a(n - 1) +/- a(n - 2)

Index entries for linear recurrences with constant coefficients, signature (199,1).

FORMULA

a(n) = 199*a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 199

a(n) = ((199+sqrt(39605))/2)^n +((199-sqrt(39605))/2)^n

(a(n))^2 = a(2n) - 2 if n = 1, 3, 5, ..., (a(n))^2 = a(2n) + 2 if n = 2, 4, 6, ...

G.f.: (2-199*x)/(1-199*x-x^2). [From Philippe Deléham, Nov 02 2008]

EXAMPLE

a(4) = 1568397607 = 199*a(3) + a(2) = 199*7881196 + 39603 = ((199+sqrt(39605))/2)^4 + ( (199-sqrt(39605))/2)^4 = 1568397606.9999999993624065 + 0.0000000006375934.

MATHEMATICA

LucasL[11*Range[0, 20]] (* or *) LinearRecurrence[{199, 1}, {2, 199}, 20] (* Harvey P. Dale, Dec 23 2015 *)

PROG

(MAGMA) [ Lucas(11*n) : n in [0..70]]; // Vincenzo Librandi, Apr 15 2011

CROSSREFS

Cf. A000032.

Sequence in context: A033147 A213162 A124339 * A280090 A195742 A180301

Adjacent sequences:  A089769 A089770 A089771 * A089773 A089774 A089775

KEYWORD

easy,nonn

AUTHOR

Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Jan 09 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 April 27 00:46 EDT 2017. Contains 285506 sequences.