A041684 Numerators of continued fraction convergents to sqrt(362).

19, 723, 27493, 1045457, 39754859, 1511730099, 57485498621, 2185960677697, 83123991251107, 3160897628219763, 120197233863602101, 4570655784445099601, 173805117042777386939, 6609165103409985803283, 251322079046622237911693, 9556848168875055026447617

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 (38,1).

Formula

From Philippe Deléham, Nov 23 2008: (Start)

a(n) = 38*a(n-1) + a(n-2), n > 1; a(0)=19, a(1)=723.

G.f.: (19+x)/(1-38*x-x^2). (End)

Mathematica

Numerator[Convergents[Sqrt[362], 30]] (* Vincenzo Librandi, Nov 06 2013 *)
LinearRecurrence[{38, 1}, {19, 723}, 20] (* Harvey P. Dale, Feb 10 2019 *)

Crossrefs

Cf. A041685.

Sequence in context: A364299 A180990 A041687 * A157165 A201708 A280625

Adjacent sequences: A041681 A041682 A041683 * A041685 A041686 A041687

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Extensions

Additional term from Colin Barker, Nov 09 2013

Status

approved