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

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 (0,12,0,-1).

Crossrefs

Cf. A010490, A041059.

Programs

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 *)

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]