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

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 (38,1).

Crossrefs

Cf. A041685.

Programs

Mathematica

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

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)

Extensions

Additional term from Colin Barker, Nov 09 2013