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

0,2

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).

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

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 *)

Prog

(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

Crossrefs

Cf. A010495, A041068.

Sequence in context: A093484 A375531 A250195 * A217053 A134590 A012978

Adjacent sequences: A041066 A041067 A041068 * A041070 A041071 A041072

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 12 2013

Status

approved