

A098260


Chebyshev polynomials S(n,627).


2



1, 627, 393128, 246490629, 154549231255, 96902121506256, 60757475635191257, 38094840321143411883, 23885404123881284059384, 14976110290833243961821885, 9389997266948320082778262511
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OFFSET

0,2


COMMENTS

Used for all positive integer solutions of Pell equation x^2  629*y^2 = 4. See A098261 with A098262.


LINKS

Table of n, a(n) for n=0..10.
Tanya Khovanova, Recursive Sequences
Index entries for sequences related to Chebyshev polynomials.
Index entries for linear recurrences with constant coefficients, signature (627, 1).


FORMULA

a(n)= S(n, 627)=U(n, 627/2)= S(2*n+1, sqrt(629))/sqrt(629) with S(n, x)=U(n, x/2) Chebyshev's polynomials of the second kind, A049310. S(1, x)= 0 = U(1, x).
a(n)=627*a(n1)a(n2), n >= 1; a(0)=1, a(1)=627; a(1):=0.
a(n)=(ap^(n+1)  am^(n+1))/(apam) with ap := (627+25*sqrt(629))/2 and am := (62725*sqrt(629))/2 = 1/ap.
G.f.: 1/(1627*x+x^2).


MATHEMATICA

LinearRecurrence[{627, 1}, {1, 627}, 20] (* Harvey P. Dale, Aug 28 2012 *)


CROSSREFS

Sequence in context: A031703 A158382 A188362 * A224603 A261708 A098261
Adjacent sequences: A098257 A098258 A098259 * A098261 A098262 A098263


KEYWORD

nonn,easy


AUTHOR

Wolfdieter Lang, Sep 10 2004


STATUS

approved



