A041123 Denominators of continued fraction convergents to sqrt(70).

1, 2, 3, 8, 11, 30, 491, 1012, 1503, 4018, 5521, 15060, 246481, 508022, 754503, 2017028, 2771531, 7560090, 123732971, 255026032, 378759003, 1012544038, 1391303041, 3795150120, 62113704961, 128022560042

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,502,0,0,0,0,0,-1).

Formula

a(n) = 502*a(n-6)-a(n-12). G.f.: -(x^2-2*x-1)*(x^8+4*x^6+15*x^4+4*x^2+1)/ (x^12-502*x^6+1). [Colin Barker, Jul 18 2012]

Mathematica

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[70], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Jun 26 2011 *)
Denominator[Convergents[Sqrt[70], 30]] (* Vincenzo Librandi, Oct 24 2013 *)

Crossrefs

Cf. A010522, A041122.

Sequence in context: A048788 A239453 A143914 * A042045 A317912 A096506

Adjacent sequences: A041120 A041121 A041122 * A041124 A041125 A041126

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved