A041029 Denominators of continued fraction convergents to sqrt(19).

1, 2, 3, 11, 14, 39, 326, 691, 1017, 3742, 4759, 13260, 110839, 234938, 345777, 1272269, 1618046, 4508361, 37684934, 79878229, 117563163, 432567718, 550130881, 1532829480, 12812766721, 27158362922

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,340,0,0,0,0,0,-1).

Formula

a(n) = 340*a(n-6)-a(n-12). G.f.: -(x^10- 2*x^9+ 3*x^8 -11*x^7 +14*x^6 -39*x^5 -14*x^4 -11*x^3 -3*x^2 -2*x -1)/(x^12-340*x^6+1). [Colin Barker, Jul 16 2012]

Mathematica

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[19], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 17 2011 *)
CoefficientList[Series[- (x^10 - 2 x^9 + 3 x^8 - 11 x^7 + 14 x^6 - 39 x^5 - 14 x^4 - 11 x^3 - 3 x^2 - 2 x - 1)/(x^12 - 340 x^6 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 22 2013 *)

Crossrefs

Cf. A010124, A010475, A041028.

Sequence in context: A242821 A182709 A321766 * A158353 A158355 A041235

Adjacent sequences: A041026 A041027 A041028 * A041030 A041031 A041032

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved