A042512 Numerators of continued fraction convergents to sqrt(785).

28, 1569, 87892, 4923521, 275805068, 15450007329, 865476215492, 48482118074881, 2715864088408828, 152136871068969249, 8522380643950686772, 477405452932307428481, 26743227744853166681708, 1498098159164709641604129, 83920240140968593096512932

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (56, 1).

Crossrefs

Cf. A042513, A040756.

Programs

Mathematica

Numerator[Convergents[Sqrt[785], 30]] (* Vincenzo Librandi, Nov 25 2013 *)

Formula

a(n) = 56*a(n-1)+a(n-2) for n>1, a(0)=28, a(1)=1569. G.f.: (28+x)/(1-56*x-x^2). [Philippe Deléham, Nov 23 2008]

Extensions

Additional term from Colin Barker, Dec 17 2013