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A097729 Pell equation solutions (6*a(n))^2 - 37*b(n)^2 = -1 with b(n):=A097730(n), n>=0. 3
1, 147, 21461, 3133159, 457419753, 66780150779, 9749444593981, 1423352130570447, 207799661618691281, 30337327244198356579, 4429041977991341369253, 646609791459491641554359, 94400600511107788325567161, 13781841064830277603891251147 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..461

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (146, -1).

FORMULA

a(n) = S(n, 2*73) + S(n-1, 2*73) = S(2*n, 2*sqrt(37)), 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, 6*I)/(6*I) with the imaginary unit I and Chebyshev polynomials of the first kind. See the T-triangle A053120.

G.f.: (1+x)/(1-2*73*x+x^2).

a(n) = 146*a(n-1)-a(n-2), n>1 ; a(0)=1, a(1)=147 . [Philippe Deléham, Nov 18 2008]

EXAMPLE

(x,y) = (6,1), (882,145), (128766,21169), ... give the positive integer solutions to x^2 - 37*y^2 =-1.

MATHEMATICA

LinearRecurrence[{146, -1}, {1, 147}, 20] (* Harvey P. Dale, Sep 24 2012 *)

CROSSREFS

Cf. A097728 for S(n, 2*73).

Sequence in context: A183741 A020328 A075925 * A214139 A215656 A214619

Adjacent sequences:  A097726 A097727 A097728 * A097730 A097731 A097732

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Aug 31 2004

EXTENSIONS

Two more terms {a(12) & a(13)) from Harvey P. Dale, Sep 24 2012

STATUS

approved

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