A042624 Numerators of continued fraction convergents to sqrt(842).

29, 1683, 97643, 5664977, 328666309, 19068310899, 1106290698451, 64183928821057, 3723774162319757, 216043085343366963, 12534222724077603611, 727200961081844376401, 42190189965471051434869, 2447758218958402827598803

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• 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 (58, 1).

Crossrefs

Cf. A042625.

Programs

Mathematica

Numerator[Convergents[Sqrt[842], 20]] (* or *) LinearRecurrence[{58, 1}, {29, 1683}, 20] (* Harvey P. Dale, Sep 24 2013 *)
CoefficientList[Series[(29 + x)/(1 - 58 x - x^2), {x, 0, 30}], x]  (* Vincenzo Librandi, Nov 30 2013 *)

Formula

a(n) = 58*a(n-1)+a(n-2) for n>1; a(0)=29, a(1)=1683. G.f.: (29+x)/(1-58*x-x^2). [Philippe Deléham, Nov 23 2008]