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A097738 Pell equation solutions (9*a(n))^2 - 82*b(n)^2 = -1 with b(n):=A097739(n), n>=0. 3
1, 327, 106601, 34751599, 11328914673, 3693191431799, 1203969077851801, 392490226188255327, 127950609768293384801, 41711506294237455189799, 13597823101311642098489673, 4432848619521301086652443599 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..397

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (326, -1).

FORMULA

a(n)= S(n, 2*163) + S(n-1, 2*163) = S(2*n, 2*sqrt(82)), with Chebyshev polynomials of the 2nd 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, 9*I)/(9*I) with the imaginary unit I and Chebyshev polynomials of the first kind. See the T-triangle A053120.

G.f.: (1+x)/(1-2*163*x+x^2).

a(n)=326*a(n-1)-a(n-2), n>1 ; a(0)=1, a(1)=327 . [From Philippe Deléham, Nov 18 2008]

EXAMPLE

(x,y) = (9*1=9;1), (2943=9*327;325), (959409=9*106601;105949), ... give the positive integer solutions to x^2 - 82*y^2 =-1.

MATHEMATICA

LinearRecurrence[{326, -1}, {1, 327}, 12] (* Ray Chandler, Aug 12 2015 *)

CROSSREFS

Cf. A097737 for S(n, 2*163).

Sequence in context: A097737 A236822 A126311 * A239536 A237505 A183848

Adjacent sequences:  A097735 A097736 A097737 * A097739 A097740 A097741

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Aug 31 2004

STATUS

approved

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Last modified June 24 16:32 EDT 2017. Contains 288707 sequences.