A041055 Denominators of continued fraction convergents to sqrt(33).

1, 1, 3, 4, 43, 47, 137, 184, 1977, 2161, 6299, 8460, 90899, 99359, 289617, 388976, 4179377, 4568353, 13316083, 17884436, 192160443, 210044879, 612250201, 822295080, 8835201001, 9657496081, 28150193163

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,46,0,0,0,-1).

Formula

a(n) = 46*a(n-4)-a(n-8). G.f.: -(x^2-x-1)*(x^4+4*x^2+1)/(x^8-46*x^4+1). [Colin Barker, Jul 16 2012]

Mathematica

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[33], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 18 2011 *)
Denominator[Convergents[Sqrt[33], 30]] (* Vincenzo Librandi, Oct 23 2013 *)
LinearRecurrence[{0, 0, 0, 46, 0, 0, 0, -1}, {1, 1, 3, 4, 43, 47, 137, 184}, 30] (* Harvey P. Dale, Apr 24 2022 *)

Crossrefs

Cf. A010488, A041054.

Sequence in context: A172144 A032837 A127614 * A246626 A032838 A013336

Adjacent sequences: A041052 A041053 A041054 * A041056 A041057 A041058

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved