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

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

Offset

0,1

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).

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]

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 *)

Crossrefs

Cf. A042625.

Sequence in context: A028478 A370679 A042627 * A190826 A045688 A084223

Adjacent sequences: A042621 A042622 A042623 * A042625 A042626 A042627

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved