login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A153885 a(n) = ((8 + sqrt(5))^n - (8 - sqrt(5))^n)/(2*sqrt(5)). 1
1, 16, 197, 2208, 23705, 249008, 2585533, 26677056, 274286449, 2814636880, 28851289589, 295557057504, 3026686834313, 30989122956272, 317251444075885, 3247664850794112, 33244802412228577, 340304612398804624, 3483430456059387941, 35656915165420734240 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Sixth binomial transform of A048879.

lim_{n -> infinity} a(n)/a(n-1) = 8 + sqrt(5) = 10.236067977499789696....

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (16, -59).

FORMULA

From Philippe Deléham, Jan 03 2009: (Start)

a(n) = 16*a(n-1) - 59*a(n-2) for n>1, with a(0)=0, a(1)=1.

G.f.: x/(1 - 16*x + 59*x^2). (End)

MATHEMATICA

Join[{a=1, b=16}, Table[c=16*b-59*a; a=b; b=c, {n, 40}]] (* Vladimir Joseph Stephan Orlovsky, Feb 08 2011*)

LinearRecurrence[{16, -59}, {1, 16}, 25] (* or *) Table[((8 + sqrt(5))^n - (8 - sqrt(5))^n)/(2*sqrt(5)) , {n, 1, 25}] (* G. C. Greubel, Aug 31 2016 *)

PROG

(Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-5); S:=[ ((8+r)^n-(8-r)^n)/(2*r): n in [1..18] ]; [ Integers()!S[j]: j in [1..#S] ]; # Klaus Brockhaus, Jan 04 2009

(Magma) I:=[1, 16]; [n le 2 select I[n] else 16*Self(n-1)-59*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Sep 01 2016

CROSSREFS

Cf. A002163 (decimal expansion of sqrt(5)), A048879.

Sequence in context: A103721 A144844 A093060 * A016226 A332854 A154240

Adjacent sequences: A153882 A153883 A153884 * A153886 A153887 A153888

KEYWORD

nonn

AUTHOR

Al Hakanson (hawkuu(AT)gmail.com), Jan 03 2009

EXTENSIONS

Extended beyond a(7) by Klaus Brockhaus, Jan 04 2009

Edited by Klaus Brockhaus, Oct 11 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 2 17:51 EST 2022. Contains 358510 sequences. (Running on oeis4.)