A042740 Numerators of continued fraction convergents to sqrt(901).

30, 1801, 108090, 6487201, 389340150, 23366896201, 1402403112210, 84167553628801, 5051455620840270, 303171504804045001, 18195341743863540330, 1092023676136616464801, 65539615909940851428390, 3933468978272587702168201, 236073678312265202981520450, 14168354167714184766593395201

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• 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 (60,1).

Crossrefs

Cf. A042741.

Programs

Mathematica

Numerator[Convergents[Sqrt[901], 30]] (* Vincenzo Librandi, Dec 03 2013 *)

Formula

From Philippe Deléham, Nov 23 2008: (Start)

a(n) = 60*a(n-1)+a(n-2) for n>1, a(0)=30, a(1)=1801.

G.f.: (30+x)/(1-60*x-x^2). (End)

E.g.f.: exp(30*x)*(30*cosh(sqrt(901)*x) + sqrt(901)*sinh(sqrt(901)*x)). - Stefano Spezia, May 14 2023