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A097766 Pell equation solutions (11*a(n))^2 - 122*b(n)^2 = -1 with b(n):=A097767(n), n>=0. 2
1, 487, 236681, 115026479, 55902632113, 27168564180439, 13203866289061241, 6417051847919582687, 3118673994222628124641, 1515669144140349348992839, 736612085378215560982395113, 357991957824668622288095032079 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (486, -1).

FORMULA

a(n)= S(n, 2*243) + S(n-1, 2*243) = S(2*n, 2*sqrt(122)), with Chebyshev polynomials of the second kind. See A049310 for the triangle of S(n, x)= U(n, x/2) coefficients. S(-1, x) := 0 =: U(-1, x).

a(n)= ((-1)^n)*T(2*n+1, 11*I)/(11*I) with the imaginary unit I and Chebyshev polynomials of the first kind. See the T-triangle A053120.

G.f.: (1+x)/(1-2*243*x+x^2).

a(n)=486*a(n-1)-a(n-2), n>1 ; a(0)=1, a(1)=487 . [From Philippe Deléham, Nov 18 2008]

EXAMPLE

(x,y) = (11*1=11;1), (5357=11*487;485), (2603491=11*236681;235709), ... give the positive integer solutions to x^2 - 122*y^2 =-1.

MATHEMATICA

LinearRecurrence[{486, -1}, {1, 487}, 12] (* Ray Chandler, Aug 12 2015 *)

CROSSREFS

Cf. A097765 for S(n, 2*243).

Sequence in context: A236424 A235839 A203873 * A214806 A126819 A045011

Adjacent sequences:  A097763 A097764 A097765 * A097767 A097768 A097769

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Aug 31 2004

STATUS

approved

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Last modified March 22 22:05 EDT 2017. Contains 283901 sequences.