A041387 Denominators of continued fraction convergents to sqrt(208).

1, 2, 5, 7, 19, 45, 1279, 2603, 6485, 9088, 24661, 58410, 1660141, 3378692, 8417525, 11796217, 32009959, 75816135, 2154861739, 4385539613, 10925940965, 15311480578, 41548902121, 98409284820, 2797008877081, 5692427038982, 14181862955045, 19874289994027

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1298,0,0,0,0,0,-1).

Formula

G.f.: -(x^4 -2*x^3 +5*x^2 +2*x +1)*(x^6 -9*x^3 -1) / ((x^2 -3*x -1)*(x^2 +3*x -1)*(x^4 -3*x^3 +10*x^2 +3*x +1)*(x^4 +3*x^3 +10*x^2 -3*x +1)). - Colin Barker, Nov 16 2013

a(n) = 1298*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 17 2013

Mathematica

Denominator[Convergents[Sqrt[208], 30]] (* Vincenzo Librandi, Dec 17 2013 *)

Prog

(Magma) I:=[1, 2, 5, 7, 19, 45, 1279, 2603, 6485, 9088, 24661, 58410]; [n le 12 select I[n] else 1298*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 17 2013

Crossrefs

Cf. A041386, A040193.

Sequence in context: A215212 A106872 A071198 * A096146 A041583 A143915

Adjacent sequences: A041384 A041385 A041386 * A041388 A041389 A041390

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 16 2013

Status

approved