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

0,1

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).

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

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 *)

Crossrefs

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

Sequence in context: A054236 A118411 A091876 * A060748 A176559 A241715

Adjacent sequences: A041063 A041064 A041065 * A041067 A041068 A041069

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved