

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
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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(n1)  a(n2), 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/(12*289*x+x^2).
a(n)= sum((1)^k*binomial(nk, k)*578^(n2*k), k=0..floor(n/2)), n>=0.
a(n) = ((289+24*sqrt(145))^(n+1)  (28924*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



