A042404 Numerators of continued fraction convergents to sqrt(730).

27, 1459, 78813, 4257361, 229976307, 12422977939, 671070785013, 36250245368641, 1958184320691627, 105778203562716499, 5713981176707382573, 308660761745761375441, 16673395115447821656387, 900671996995928130820339, 48652961232895566885954693

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 (54, 1).

Crossrefs

Cf. A042405, A040702.

Programs

Mathematica

Numerator[Convergents[Sqrt[730], 30]] (* Vincenzo Librandi, Nov 23 2013 *)
LinearRecurrence[{54,1},{27,1459},20] (* Harvey P. Dale, Nov 29 2020 *)

Formula

a(n)=54*a(n-1)+a(n-2), n>1; a(0)=27, a(1)=1459. G.f.: (27+x)/(1-54*x-x^2). - Philippe Deléham, Nov 23 2008

Extensions

a(14) from Colin Barker, Dec 11 2013