

A098244


First differences of Chebyshev polynomials S(n,171)=A097844(n) with Diophantine property.


5



1, 170, 29069, 4970629, 849948490, 145336221161, 24851643870041, 4249485765555850, 726637214266180309, 124250714153751276989, 21246145483077202184810, 3632966626892047822325521
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OFFSET

0,2


COMMENTS

(13*b(n))^2  173*a(n)^2 = 4 with b(n)=A097845(n) give all positive solutions of this Pell equation.


LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..446
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (171, 1).
Index entries for sequences related to Chebyshev polynomials.


FORMULA

a(n) = ((1)^n)*S(2*n, 13*I) with the imaginary unit I and the S(n, x)=U(n, x/2) Chebyshev polynomials.
G.f.: (1x)/(1171*x+x^2).
a(n) = S(n, 171)  S(n1, 171) = T(2*n+1, sqrt(173)/2)/(sqrt(173)/2), with S(n, x)=U(n, x/2) Chebyshev's polynomials of the second kind, A049310. S(1, x)= 0 = U(1, x) and T(n, x) Chebyshev's polynomials of the first kind, A053120.
a(n) = 171*a(n1)a(n2), n>1 ; a(0)=1, a(1)=170 . [Philippe Deléham, Nov 18 2008]


EXAMPLE

All positive solutions of Pell equation x^2  173*y^2 = 4 are (13=13*1,1), (2236=13*172,170), (382343=13*29411,29069), (65378417=13*5029109,4970629), ...


CROSSREFS

Sequence in context: A210784 A178499 A133328 * A250957 A114048 A187704
Adjacent sequences: A098241 A098242 A098243 * A098245 A098246 A098247


KEYWORD

nonn,easy


AUTHOR

Wolfdieter Lang, Sep 10 2004


STATUS

approved



