A041066 Numerators of continued fraction convergents to sqrt(40).

6, 19, 234, 721, 8886, 27379, 337434, 1039681, 12813606, 39480499, 486579594, 1499219281, 18477210966, 56930852179, 701647437114, 2161873163521, 26644125399366, 82094249361619, 1011775117738794

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

Comments

With a(-1) = 1, a(n-1) gives, for n >= 0, the denominator of the convergents to 1/sqrt(40) = 1/(2*sqrt(10)). - Wolfdieter Lang, Nov 21 2017

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100
• Index entries for linear recurrences with constant coefficients, signature (0,38,0,-1).

Crossrefs

Cf. A041067 (denominators), A010494, A020797 (1/sqrt(40)).

Programs

Mathematica

Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[40],n]]],{n,1,50}] (* Vladimir Joseph Stephan Orlovsky, Mar 21 2011*)
Numerator[Convergents[Sqrt[40], 30]] (* Vincenzo Librandi, Oct 29 2013 *)
LinearRecurrence[{0,38,0,-1},{6,19,234,721},20] (* Harvey P. Dale, Jul 20 2024 *)

Formula

G.f.: -(x+2)*(x^2-8*x-3) / ((x^2-6*x-1)*(x^2+6*x-1)). - Colin Barker, Nov 04 2013