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

0,1

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 (60,1).

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

Mathematica

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

Crossrefs

Cf. A042741.

Sequence in context: A202384 A202369 A042743 * A367392 A282126 A112003

Adjacent sequences: A042737 A042738 A042739 * A042741 A042742 A042743

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Status

approved