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A098249 Chebyshev polynomials S(n,291) + S(n-1,291) with Diophantine property. 3
1, 292, 84971, 24726269, 7195259308, 2093795732359, 609287362857161, 177300528795701492, 51593844592186277011, 15013631475797410908709, 4368915165612454388157308, 1271339299561748429542867919 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

(17*a(n))^2 - 293*b(n)^2 = -4 with b(n)=A098250(n) give all positive solutions of this Pell equation.

LINKS

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

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

FORMULA

a(n)= (-2/17)*I*((-1)^n)*T(2*n+1, 17*I/2) with the imaginary unit I and Chebyshev's polynomials of the first kind. See the T-triangle A053120.

G.f.: (1+x)/(1-291*x+x^2).

a(n)= S(n, 291) + S(n-1, 291) = S(2*n, sqrt(293)), with S(n, x)=U(n, x/2) Chebyshev's polynomials of the second kind, A049310. S(-1, x)= 0 = U(-1, x). S(n, 227)=A098245(n).

a(n)=291*a(n-1)-a(n-2), n>1 ; a(0)=1, a(1)=292 . [From Philippe Deléham, Nov 18 2008]

EXAMPLE

All positive solutions of Pell equation x^2 - 293*y^2 = -4 are

(17=17*1,1), (4964=17*292,290), (1444507=17*84971,84389),

(420346573=17*24726269,24556909), ...

CROSSREFS

Sequence in context: A221832 A238321 A231662 * A190925 A232280 A202888

Adjacent sequences:  A098246 A098247 A098248 * A098250 A098251 A098252

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Sep 10 2004

STATUS

approved

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Last modified November 27 11:59 EST 2014. Contains 250196 sequences.