A041420 Numerators of continued fraction convergents to sqrt(226).

15, 451, 13545, 406801, 12217575, 366934051, 11020239105, 330974107201, 9940243455135, 298538277761251, 8966088576292665, 269281195566541201, 8087401955572528695, 242891339862742402051, 7294827597837844590225, 219087719274998080108801

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 (30,1).

Crossrefs

Cf. A041421.

Programs

Mathematica

Numerator[Convergents[Sqrt[226], 20]] (* Harvey P. Dale, Feb 02 2012 *)

Formula

a(n) = 30*a(n-1)+a(n-2), n>1 ; a(0)=15, a(1)=451 . G.f.: (15+x)/(1-30*x-x^2). - Philippe Deléham, Nov 22 2008

Extensions

Additional term from Colin Barker, Nov 07 2013