A041069 Denominators of continued fraction convergents to sqrt(41).

1, 2, 5, 62, 129, 320, 3969, 8258, 20485, 254078, 528641, 1311360, 16264961, 33841282, 83947525, 1041211582, 2166370689, 5373952960, 66653806209, 138681565378, 344016936965, 4266884808958, 8877786554881, 22022457918720, 273147281579521, 568317021077762

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 (0,0,64,0,0,1).

Crossrefs

Cf. A010495, A041068.

Programs

Magma

I:=[1, 2, 5, 62, 129, 320]; [n le 6 select I[n] else 64*Self(n-3)+Self(n-6): n in [1..30]]; // Vincenzo Librandi, Dec 10 2013

Mathematica

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[41], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 21 2011 *)
Denominator[Convergents[Sqrt[41], 30]] (* Vincenzo Librandi, Dec 10 2013 *)
LinearRecurrence[{0,0,64,0,0,1},{1,2,5,62,129,320},40] (* Harvey P. Dale, Jun 19 2022 *)

Formula

G.f.: -(x^4-2*x^3+5*x^2+2*x+1) / (x^6+64*x^3-1). - Colin Barker, Nov 12 2013

a(n) = 64*a(n-3) + a(n-6). - Vincenzo Librandi, Dec 10 2013

Extensions

More terms from Colin Barker, Nov 12 2013