A041068 Numerators of continued fraction convergents to sqrt(41).

6, 13, 32, 397, 826, 2049, 25414, 52877, 131168, 1626893, 3384954, 8396801, 104146566, 216689933, 537526432, 6667007117, 13871540666, 34410088449, 426792602054, 887995292557, 2202783187168, 27321393538573

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100
• Index entries for linear recurrences with constant coefficients, signature (0,0,64,0,0,1).

Crossrefs

Cf. A041069, A010495.

Programs

Mathematica

Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[41],n]]],{n,1,50}] (* Vladimir Joseph Stephan Orlovsky, Mar 21 2011*)
Numerator[Convergents[Sqrt[41], 30]] (* Vincenzo Librandi, Oct 29 2013 *)
LinearRecurrence[{0,0,64,0,0,1},{6,13,32,397,826,2049},30] (* Harvey P. Dale, Mar 17 2019 *)

Formula

G.f.: -(x^5-6*x^4+13*x^3+32*x^2+13*x+6) / (x^6+64*x^3-1). - Colin Barker, Nov 04 2013