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A097775 Pell equation solutions (14*a(n))^2 - 197*b(n)^2 = -1 with b(n) = A097776(n), n>=0. 3
1, 787, 618581, 486203879, 382155630313, 300373839222139, 236093455472970941, 185569155627915937487, 145857120230086453893841, 114643510931692324844621539, 90109653735189937241418635813, 70826073192348358979430203127479, 55669203419532074967894898239562681 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Colin Barker, Table of n, a(n) for n = 0..345

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

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

FORMULA

a(n) = S(n, 2*393) + S(n-1, 2*393) = S(2*n, 2*sqrt(197)), 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, 14*I)/(14*I) with the imaginary unit I and Chebyshev polynomials of the first kind. See the T-triangle A053120.

G.f.: (1+x)/(1-2*393*x+x^2).

a(n) = 786*a(n-1)-a(n-2) for n>1 ; a(0)=1, a(1)=787. - 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.

PROG

(PARI) Vec((1+x)/(1-2*393*x+x^2) + O(x^100)) \\ Colin Barker, Apr 04 2015

CROSSREFS

Cf. A097774 for S(n, 2*393).

Sequence in context: A045231 A267476 A068660 * A072730 A180100 A072722

Adjacent sequences:  A097772 A097773 A097774 * A097776 A097777 A097778

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.