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

0,1

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.: (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

Mathematica

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

Crossrefs

Cf. A010471, A041021.

Sequence in context: A042327 A046114 A116654 * A041527 A290493 A266384

Adjacent sequences: A041017 A041018 A041019 * A041021 A041022 A041023

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Status

approved