OFFSET
0,2
LINKS
Indranil Ghosh, Table of n, a(n) for n = 0..461
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 (146,-1).
FORMULA
G.f.: (1 + x)/(1 - 2*73*x + x^2).
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.
a(n) = 146*a(n-1) - a(n-2), n > 1; a(0)=1, a(1)=147. - Philippe Deléham, Nov 18 2008
a(n) = (1/6)*sinh((2*n + 1)*arcsinh(6)). - Bruno Berselli, Apr 03 2018
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 *)
PROG
(PARI) x='x+O('x^99); Vec((1+x)/(1-2*73*x+x^2)) \\ Altug Alkan, Apr 05 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Aug 31 2004
EXTENSIONS
a(12)-a(13) from Harvey P. Dale, Sep 24 2012
STATUS
approved