A041021 Denominators of continued fraction convergents to sqrt(14).

1, 1, 3, 4, 27, 31, 89, 120, 809, 929, 2667, 3596, 24243, 27839, 79921, 107760, 726481, 834241, 2394963, 3229204, 21770187, 24999391, 71768969, 96768360, 652379129, 749147489, 2150674107, 2899821596

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,30,0,0,0,-1).

Formula

G.f.: (1+1*x+3*x^2+4*x^3-3*x^4+x^5-x^6)/(1-30*x^4+x^8). [Colin Barker, Jan 03 2012]

Mathematica

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[14], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 17 2011*)
Convergents[Sqrt[14], 30]//Denominator (* or *) LinearRecurrence[{0, 0, 0, 30, 0, 0, 0, -1}, {1, 1, 3, 4, 27, 31, 89, 120}, 30] (* Harvey P. Dale, Aug 17 2024 *)

Crossrefs

Cf. A010471, A041020.

Sequence in context: A300373 A222112 A032832 * A041022 A157163 A042225

Adjacent sequences: A041018 A041019 A041020 * A041022 A041023 A041024

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved