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A098261 Chebyshev polynomials S(n,627) + S(n-1,627) with Diophantine property. 2
1, 628, 393755, 246883757, 154795721884, 97056670737511, 60854377756697513, 38155597796778603140, 23923498964202427471267, 14999995694957125245881269, 9404973377239153326740084396 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

(25*a(n))^2 - 629*b(n)^2 = -4 with b(n)=A098262(n) give all positive solutions of this Pell equation.

LINKS

Table of n, a(n) for n=0..10.

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (627, -1).

Index entries for sequences related to Chebyshev polynomials.

FORMULA

a(n)= S(n, 627) + S(n-1, 627) = S(2*n, 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). S(n, 531)=A098260(n).

a(n)= (-2/25)*I*((-1)^n)*T(2*n+1, 25*I/2) with the imaginary unit I and Chebyshev's polynomials of the first kind. See the T-triangle A053120.

G.f.: (1+x)/(1-627*x+x^2).

a(n)=627*a(n-1)-a(n-2), n>1 ; a(0)=1, a(1)=628 . [From Philippe Deléham, Nov 18 2008]

EXAMPLE

All positive solutions of Pell equation x^2 - 629*y^2 = -4 are

(25=25*1,1), (15700=25*628,626), (9843875=25*393755,392501),

(6172093925=25*246883757,246097501), ...

CROSSREFS

Sequence in context: A098260 A224603 A261708 * A256937 A177421 A173423

Adjacent sequences:  A098258 A098259 A098260 * A098262 A098263 A098264

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Sep 10 2004

STATUS

approved

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Last modified May 23 22:04 EDT 2017. Contains 286937 sequences.