OFFSET
0,1
COMMENTS
x = a(n) and y' = b(n) := A226700(n) are the improper and proper nonnegative solutions x^2 - 61*(3*5*13*y')^2 = +4.
REFERENCES
T. Nagell, Introduction to Number Theory, Chelsea Publishing Company, New York, 1964, ch. Vi, 58., p. 204-212.
LINKS
FORMULA
a(n) = 2*S(n,1523) - 1523*S(n-1,1523), n >= 0, with the Chebyshev S-polynomials (A049310).
O.g.f.: (2- 1523*x)/(1- 1523*x + x^2).
a(n) = 1523*a(n-1) - a(n-2), n >= 1, a(-1) = 1523, a(0) = 2.
EXAMPLE
n=0: 2^2 - 0 = +4 (improper),
n=1: 1523^2 - 61*(3*5*13*1)^2 = +4,
n=2: 2319527^2 - 61*(3*5*13*1523)^2 = +4.
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Jun 27 2013
STATUS
approved