A041037 Denominators of continued fraction convergents to sqrt(23).

1, 1, 4, 5, 44, 49, 191, 240, 2111, 2351, 9164, 11515, 101284, 112799, 439681, 552480, 4859521, 5412001, 21095524, 26507525, 233155724, 259663249, 1012145471, 1271808720, 11186615231, 12458423951

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,48,0,0,0,-1).

Formula

G.f.: (1+x+4*x^2+5*x^3-4*x^4+x^5-x^6)/(1-48*x^4+x^8). [Colin Barker, Jan 03 2012]

Mathematica

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[23], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 17 2011 *)
Denominator[Convergents[Sqrt[23], 30]] (* or *) LinearRecurrence[ {0, 0, 0, 48, 0, 0, 0, -1}, {1, 1, 4, 5, 44, 49, 191, 240}, 30] (* Harvey P. Dale, Jun 22 2021 *)

Crossrefs

Cf. A010479, A041036.

Sequence in context: A270129 A271293 A256290 * A041038 A239860 A151486

Adjacent sequences: A041034 A041035 A041036 * A041038 A041039 A041040

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved