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A097730 Pell equation solutions (6*b(n))^2 - 37*a(n)^2 = -1 with b(n):=A097729(n), n>=0. 5
1, 145, 21169, 3090529, 451196065, 65871534961, 9616792908241, 1403985893068225, 204972323595052609, 29924555258984612689, 4368780095488158399985, 637811969386012141785121 (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) = T(2*n+1, sqrt(37)/sqrt(37), 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, 12*I) with the imaginary unit I and Chebyshev polynomials S(n, x) with coefficients shown in A049310.

G.f.: (1-x)/(1-146*x+x^2).

a(n) = 146*a(n-1)-a(n-2), n>1 ; a(0)=1, a(1)=145 . [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, 145}, 12] (* Ray Chandler, Aug 12 2015 *)

CROSSREFS

Cf. A097729 for S(n, 146).

Row 6 of array A188647.

Sequence in context: A031612 A226849 A018232 * A283520 A265439 A060720

Adjacent sequences:  A097727 A097728 A097729 * A097731 A097732 A097733

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.