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!)
A157666 a(n) = 19683*n - 13716. 3
5967, 25650, 45333, 65016, 84699, 104382, 124065, 143748, 163431, 183114, 202797, 222480, 242163, 261846, 281529, 301212, 320895, 340578, 360261, 379944, 399627, 419310, 438993, 458676, 478359, 498042, 517725, 537408, 557091, 576774, 596457 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (531441*n^2 - 740664*n + 258065)^2 - (729*n^2 - 1016*n + 354)*(19683*n - 13716)^2 = 1 can be written as A157667(n)^2 - A157665(n)*a(n)^2 = 1.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Vincenzo Librandi, X^2-AY^2=1

Index entries for linear recurrences with constant coefficients, signature (2,-1).

FORMULA

From Harvey P. Dale, Nov 03 2011: (Start)

G.f.: 27*x*(508*x+221)/(x-1)^2.

a(n) = 2*a(n-1) - a(n-2); a(1)=5967, a(2)=25650. (End)

E.g.f.: 27*(508 - (508 - 729*x)*exp(x)). - G. C. Greubel, Nov 17 2018

EXAMPLE

a(1) = 19683*1 - 13716 = 5967;

a(2) = 19683*2 - 13716 = 25650.

MATHEMATICA

19683Range[40]-13716 (* or *) LinearRecurrence[{2, -1}, {5967, 25650}, 40] (* Harvey P. Dale, Nov 03 2011 *)

PROG

(Magma) I:=[5967, 25650]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..40]];

(PARI) a(n) = 19683*n - 13716.

(Sage) [19683*n-13716 for n in (1..40)] # G. C. Greubel, Nov 17 2018

(GAP) List([1..40], n -> 19683*n-13716); # G. C. Greubel, Nov 17 2018

CROSSREFS

Cf. A157665, A157667.

Sequence in context: A186479 A266038 A032658 * A176374 A282191 A328327

Adjacent sequences: A157663 A157664 A157665 * A157667 A157668 A157669

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 04 2009

EXTENSIONS

Example edited by Jon E. Schoenfield, Nov 17 2018

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 3 11:24 EST 2022. Contains 358517 sequences. (Running on oeis4.)