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A098250 First differences of Chebyshev polynomials S(n,291)=A098248(n) with Diophantine property. 5
1, 290, 84389, 24556909, 7145976130, 2079454496921, 605114112627881, 176086127320216450, 51240457936070359069, 14910797173269154272629, 4338990736963387822975970, 1262631393659172587331734641 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

(17*b(n))^2 - 293*a(n)^2 = -4 with b(n)=A098249(n) give all positive solutions of this Pell equation.

LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..405

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (291,-1).

Index entries for sequences related to Chebyshev polynomials.

FORMULA

a(n)= ((-1)^n)*S(2*n, 17*I) with the imaginary unit I and the S(n, x)=U(n, x/2) Chebyshev polynomials.

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

a(n)= S(n, 291) - S(n-1, 291) = T(2*n+1, sqrt(293)/2)/(sqrt(293)/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)=291*a(n-1)-a(n-2), n>1 ; a(0)=1, a(1)=290 . [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: A237741 A186548 A091740 * A031515 A090890 A123913

Adjacent sequences:  A098247 A098248 A098249 * A098251 A098252 A098253

KEYWORD

nonn,easy,changed

AUTHOR

Wolfdieter Lang, Sep 10 2004

STATUS

approved

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Last modified March 25 13:25 EDT 2017. Contains 284080 sequences.