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

0,1

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).

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

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 *)

Crossrefs

Cf. A041069, A010495.

Sequence in context: A147330 A042607 A048693 * A300430 A300634 A301356

Adjacent sequences: A041065 A041066 A041067 * A041069 A041070 A041071

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved