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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

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Last modified June 27 19:44 EDT 2017. Contains 288790 sequences.