A041020 Numerators of continued fraction convergents to sqrt(14).

3, 4, 11, 15, 101, 116, 333, 449, 3027, 3476, 9979, 13455, 90709, 104164, 299037, 403201, 2718243, 3121444, 8961131, 12082575, 81456581, 93539156, 268534893, 362074049, 2440979187, 2803053236, 8047085659

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

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, A041021.

Programs

Mathematica

Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[14],n]]],{n,1,50}] (* Vladimir Joseph Stephan Orlovsky, Mar 17 2011*)

Formula

G.f.: (3+4*x+11*x^2+15*x^3+11*x^4-4*x^5+3*x^6-x^7)/(1-30*x^4+x^8). - Colin Barker, Jan 03 2012

a(n) = 30*a(n-4) - a(n-8). - Wesley Ivan Hurt, Aug 04 2025