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!)
A114052 x such that x^2 - 27*y^2 = 1. 1
1, 26, 1351, 70226, 3650401, 189750626, 9863382151, 512706121226, 26650854921601, 1385331749802026, 72010600134783751, 3743165875258953026, 194572614913330773601, 10114032809617941274226, 525735133485219615486151 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A Pellian equation (Pell's equation). - Benoit Cloitre, Feb 03 2006

LINKS

Robert Israel, Table of n, a(n) for n = 0..524

Tanya Khovanova, Recursive Sequences

John Robertson, Home page.

Index entries for linear recurrences with constant coefficients, signature (52,-1).

FORMULA

a(0) = 1, a(1) = 26 then a(n) = 52*a(n-1) - a(n-2). - Benoit Cloitre, Feb 03 2006

G.f.: (1 - 26x)/(1 - 52x + x^2). - Philippe Deléham, Nov 18 2008

a(n) = 1/2*(1+(26+15*sqrt(3))^(2*n))/(26+15*sqrt(3))^n. - Gerry Martens, May 30 2015

MAPLE

f:= gfun:-rectoproc({a(n)=52*a(n-1)-a(n-2), a(0)=1, a(1)=26}, a(n), remember):

map(f, [$0..40]); # Robert Israel, Jun 01 2015

MATHEMATICA

A114052[n_] := 1/2(1 + (26 + 15 Sqrt[3])^(2 n))/(26 + 15 Sqrt[3])^n; Table[A114052[n] // FullSimplify, {n, 0, 20}] (* Gerry Martens, May 30 2015 *)

CoefficientList[Series[(1 - 26 x)/(1 - 52 x + x^2), {x, 0, 33}], x] (* Vincenzo Librandi, May 31 2015 *)

PROG

(PARI) g(n, k) = for(y=0, n, x=k*y^2+1; if(issquare(x), print1(floor(sqrt(x))", ")))

(PARI) a0=1; a1=26; for(n=2, 30, a2=52*a1-a0; a0=a1; a1=a2; print1(a2, ", ")) \\ Benoit Cloitre, Feb 03 2006

(MAGMA)  I:=[1, 26]; [n le 2 select I[n] else 52*Self(n-1)-Self(n-2): n in [1..30]]; // Vincenzo Librandi, May 31 2015

CROSSREFS

Sequence in context: A160311 A220955 A106710 * A042303 A042300 A282884

Adjacent sequences:  A114049 A114050 A114051 * A114053 A114054 A114055

KEYWORD

easy,nonn

AUTHOR

Cino Hilliard, Feb 01 2006

EXTENSIONS

More terms from Benoit Cloitre, Feb 03 2006

More terms from Robert G. Wilson v, Mar 17 2006

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.