A041058 Numerators of continued fraction convergents to sqrt(35).

5, 6, 65, 71, 775, 846, 9235, 10081, 110045, 120126, 1311305, 1431431, 15625615, 17057046, 186196075, 203253121, 2218727285, 2421980406, 26438531345, 28860511751, 315043648855, 343904160606, 3754085254915

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,12,0,-1).

Formula

a(n) = 12*a(n-2)-a(n-4). G.f.: (5+6*x+5*x^2-x^3)/(1-12*x^2+x^4). [Colin Barker, Apr 17 2012]

Mathematica

Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[35], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 21 2011 *)
Numerator[Convergents[Sqrt[35], 30]] (* Vincenzo Librandi, Oct 23 2013 *)

Crossrefs

Cf. A010490, A041059.

Sequence in context: A132444 A111504 A041057 * A322844 A259299 A328561

Adjacent sequences: A041055 A041056 A041057 * A041059 A041060 A041061

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved