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A097739 Pell equation solutions (9*b(n))^2 - 82*a(n)^2 = -1 with b(n):=A097738(n), n>=0. 5
1, 325, 105949, 34539049, 11259624025, 3670602893101, 1196605283526901, 390089651826876625, 127168029890278252849, 41456387654578883552149, 13514655207362825759747725, 4405736141212626618794206201 (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) = T(2*n+1, sqrt(82))/sqrt(82), with Chebyshev polynomials of the 2nd and first kind. See A049310 for the triangle of S(n, x)= U(n, x/2) coefficients. S(-1, x) := 0 =: U(-1, x); and A053120 for the T-triangle.

a(n)= ((-1)^n)*S(2*n, 18*I) with the imaginary unit I and Chebyshev polynomials S(n, x) with coefficients shown in A049310.

G.f.: (1-x)/(1- 326*x+x^2).

a(n)=326*a(n-1)-a(n-2), n>1 ; a(0)=1, a(1)=325 . [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, 325}, 12] (* Ray Chandler, Aug 12 2015 *)

CROSSREFS

Cf. A097737 for S(n, 326).

Row 9 of array A188647.

Sequence in context: A166220 A121000 A048909 * A203188 A048918 A274307

Adjacent sequences:  A097736 A097737 A097738 * A097740 A097741 A097742

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Aug 31 2004

STATUS

approved

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Last modified April 30 08:33 EDT 2017. Contains 285645 sequences.