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A041066
Numerators of continued fraction convergents to sqrt(40).
3
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
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 *)
LinearRecurrence[{0, 38, 0, -1}, {6, 19, 234, 721}, 20] (* Harvey P. Dale, Jul 20 2024 *)
CROSSREFS
Cf. A041067 (denominators), A010494, A020797 (1/sqrt(40)).
Sequence in context: A054236 A118411 A091876 * A060748 A176559 A241715
KEYWORD
nonn,cofr,frac,easy
AUTHOR
STATUS
approved