OFFSET
0,2
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..372
Tanya Khovanova, Recursive Sequences
Giovanni Lucca, Integer Sequences and Circle Chains Inside a Hyperbola, Forum Geometricorum (2019) Vol. 19, 11-16.
Index entries for linear recurrences with constant coefficients, signature (486,-1).
FORMULA
G.f.: (1 + x)/(1 - 2*243*x + x^2).
a(n) = S(n, 2*243) + S(n-1, 2*243) = S(2*n, 2*sqrt(122)), 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, 11*i)/(11*i) with the imaginary unit i and Chebyshev polynomials of the first kind. See the T-triangle A053120.
a(n) = 486*a(n-1) - a(n-2), n > 1; a(0)=1, a(1)=487. - Philippe Deléham, Nov 18 2008
a(n) = (1/11)*sinh((2*n + 1)*arcsinh(11)). - Bruno Berselli, Apr 03 2018
EXAMPLE
(x,y) = (11*1=11;1), (5357=11*487;485), (2603491=11*236681;235709), ... give the positive integer solutions to x^2 - 122*y^2 =-1.
MATHEMATICA
LinearRecurrence[{486, -1}, {1, 487}, 12] (* Ray Chandler, Aug 12 2015 *)
PROG
(PARI) x='x+O('x^99); Vec((1+x)/(1-2*243*x+x^2)) \\ Altug Alkan, Apr 05 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Aug 31 2004
STATUS
approved