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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A097766 Pell equation solutions (11*a(n))^2 - 122*b(n)^2 = -1 with b(n):=A097767(n), n>=0. 4
1, 487, 236681, 115026479, 55902632113, 27168564180439, 13203866289061241, 6417051847919582687, 3118673994222628124641, 1515669144140349348992839, 736612085378215560982395113, 357991957824668622288095032079, 173983354890703572216453203195281 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..372

Tanya Khovanova, Recursive Sequences

Giovanni Lucca, Integer Sequences and Circle Chains Inside a Hyperbola, Forum Geometricorum (2019) Vol. 19, 11-16.

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (486,-1).

FORMULA

G.f.: (1 + x)/(1 - 2*243*x + x^2).

a(n) = S(n, 2*243) + S(n-1, 2*243) = S(2*n, 2*sqrt(122)), with Chebyshev polynomials of the second kind. See A049310 for the triangle of S(n, x)= U(n, x/2) coefficients. S(-1, x) := 0 =: U(-1, x).

a(n) = ((-1)^n)*T(2*n+1, 11*I)/(11*I) with the imaginary unit I and Chebyshev polynomials of the first kind. See the T-triangle A053120.

a(n) = 486*a(n-1)-a(n-2), n>1; a(0)=1, a(1)=487. - Philippe Deléham, Nov 18 2008

a(n) = (1/11)*sinh((2*n + 1)*arcsinh(11)). - Bruno Berselli, Apr 03 2018

EXAMPLE

(x,y) = (11*1=11;1), (5357=11*487;485), (2603491=11*236681;235709), ... give the positive integer solutions to x^2 - 122*y^2 =-1.

MATHEMATICA

LinearRecurrence[{486, -1}, {1, 487}, 12] (* Ray Chandler, Aug 12 2015 *)

PROG

(PARI) x='x+O('x^99); Vec((1+x)/(1-2*243*x+x^2)) \\ Altug Alkan, Apr 05 2018

CROSSREFS

Cf. A097765 for S(n, 2*243).

Cf. similar sequences of the type (1/k)*sinh((2*n+1)*arcsinh(k)) listed in A097775.

Sequence in context: A236424 A235839 A203873 * A214806 A126819 A045011

Adjacent sequences:  A097763 A097764 A097765 * A097767 A097768 A097769

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Aug 31 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 09:33 EST 2019. Contains 329843 sequences. (Running on oeis4.)