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

 

Logo

The OEIS is looking to hire part-time people to help edit core sequences, upload scanned documents, process citations, fix broken links, etc. - Neil Sloane, njasloane@gmail.com

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A065705 a(n) = Lucas(10*n). 3
2, 123, 15127, 1860498, 228826127, 28143753123, 3461452808002, 425730551631123, 52361396397820127, 6440026026380244498, 792070839848372253127, 97418273275323406890123, 11981655542024930675232002, 1473646213395791149646646123, 181246502592140286475862241127 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Lim_{n->infinity} a(n+1)/a(n) = (123 + sqrt(15125))/2 = 122.9918693812...

Lim_{n->infinity} a(n)/a(n+1) = (123 - sqrt(15125))/2 = 0.00813061875578...

LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..477

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 (123,-1).

FORMULA

a(n) = 123*a(n-1) - a(n-2), starting with a(0) = 2 and a(1) = 123.

a(n) = ((123 + sqrt(15125))/2)^n + ((123 - sqrt(15125))/2)^n.

a(n)^2 = a(2*n) + 2.

G.f.: (2 - 123*x)/(1 - 123*x + x^2). -  Philippe Deléham, Nov 18 2008

EXAMPLE

a(4) = 228826127 = 123*a(3) - a(2) = 123*1860498 - 15127=((123+sqrt(15125))/2)^4 + ( (123-sqrt(15125))/2)^4 =228826126.99999999562986 + 0.00000000437013 = 228826127.

a(4) = L(10 * 4) = L(40) = 228826127. - Indranil Ghosh, Feb 08 2017

PROG

(MAGMA) [Lucas(10*n): n in [0..90]]; // Vincenzo Librandi, Apr 14 2011

CROSSREFS

Cf. A000032: a(n) = A000032(10*n).

Sequence in context: A230586 A024244 A088055 * A012870 A183720 A042921

Adjacent sequences:  A065702 A065703 A065704 * A065706 A065707 A065708

KEYWORD

nonn,easy

AUTHOR

Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Oct 25 2003

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 May 28 19:46 EDT 2017. Contains 287241 sequences.