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A097776 Pell equation solutions (14*b(n))^2 - 197*a(n)^2 = -1 with b(n):=A097775(n), n>=0. 3
1, 785, 617009, 484968289, 381184458145, 299610499133681, 235493471134615121, 185097568701308351425, 145486453505757229604929, 114352167357956481161122769, 89880658056900288435412891505 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..10.

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (786,-1).

Index entries for sequences related to Chebyshev polynomials.

FORMULA

a(n)= S(n, 2*393) - S(n-1, 2*393) = T(2*n+1, sqrt(197))/sqrt(197), 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, 28*I) with the imaginary unit I and Chebyshev polynomials S(n, x) with coefficients shown in A049310.

G.f.: (1-x)/(1-786*x+x^2).

a(n)=786*a(n-1)-a(n-2), n>1 ; a(0)=1, a(1)=785 . [From Philippe Deléham, Nov 18 2008]

EXAMPLE

(x,y) = (14*1=14;1), (11018=14*787;785), (8660134=14*618581;617009), ... give the positive integer solutions to x^2 - 197*y^2 =-1.

CROSSREFS

Cf. A097774 for S(n, 786).

Sequence in context: A159896 A031734 A031616 * A031526 A108795 A097774

Adjacent sequences:  A097773 A097774 A097775 * A097777 A097778 A097779

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.