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, 19549603683, 22449425279, 64448454241, 86897879520

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy
• changed

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).

Crossrefs

Cf. A010471, A041020, A157878 (quadrisection), A068204 (quadrisection).

Programs

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 *)

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