A041641 Denominators of continued fraction convergents to sqrt(339).

1, 2, 5, 12, 17, 301, 318, 937, 2192, 5321, 193748, 392817, 979382, 2351581, 3330963, 58977952, 62308915, 183595782, 429500479, 1042596740, 37962983119, 76968562978, 191900109075, 460768781128, 652668890203, 11556139914579, 12208808804782

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,195940,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^18 -2*x^17 +5*x^16 -12*x^15 +17*x^14 -301*x^13 +318*x^12 -937*x^11 +2192*x^10 -5321*x^9 -2192*x^8 -937*x^7 -318*x^6 -301*x^5 -17*x^4 -12*x^3 -5*x^2 -2*x -1) / (x^20 -195940*x^10 +1). - Colin Barker, Nov 20 2013

a(n) = 195940*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Dec 22 2013

Mathematica

Denominator[Convergents[Sqrt[339], 30]] (* Vincenzo Librandi, Dec 22 2013 *)

Prog

(Magma) I:=[1, 2, 5, 12, 17, 301, 318, 937, 2192, 5321, 193748, 392817, 979382, 2351581, 3330963, 58977952, 62308915, 183595782, 429500479, 1042596740]; [n le 20 select I[n] else 195940*Self(n-10) - Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 22 2013

Crossrefs

Cf. A041640, A040320.

Sequence in context: A055906 A002355 A085395 * A131091 A356490 A336462

Adjacent sequences: A041638 A041639 A041640 * A041642 A041643 A041644

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 20 2013

Status

approved