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!)
A097768 Chebyshev U(n,x) polynomial evaluated at x=289=2*12^2+1. 2
1, 578, 334083, 193099396, 111611116805, 64511032413894, 37287265124113927, 21551974730705435912, 12457004107082617843209, 7200126821919022407938890, 4161660846065087869170835211, 2405432768898798869358334813068 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Used to form integer solutions of Pell equation a^2 - 145*b^2 =-1. See A097769 with A097770.

LINKS

Table of n, a(n) for n=0..11.

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (578, -1).

FORMULA

a(n) = 2*289*a(n-1) - a(n-2), n>=1, a(0)=1, a(-1):=0.

a(n) = S(n, 2*289)= U(n, 289), Chebyshev's polynomials of the second kind. See A049310.

G.f.: 1/(1-2*289*x+x^2).

a(n)= sum((-1)^k*binomial(n-k, k)*578^(n-2*k), k=0..floor(n/2)), n>=0.

a(n) = ((289+24*sqrt(145))^(n+1) - (289-24*sqrt(145))^(n+1))/(48*sqrt(145)), n>=0.

MATHEMATICA

LinearRecurrence[{578, -1}, {1, 578}, 12] (* Ray Chandler, Aug 12 2015 *)

CROSSREFS

Sequence in context: A232888 A035754 A107550 * A286233 A073735 A250727

Adjacent sequences:  A097765 A097766 A097767 * A097769 A097770 A097771

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 12 09:36 EST 2019. Contains 329953 sequences. (Running on oeis4.)