A041609 Denominators of continued fraction convergents to sqrt(322).

1, 1, 17, 18, 629, 647, 10981, 11628, 406333, 417961, 7093709, 7511670, 262490489, 270002159, 4582525033, 4852527192, 169568449561, 174420976753, 2960304077609, 3134725054362, 109540955925917, 112675680980279, 1912351851610381, 2025027532590660

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,646,0,0,0,-1).

Formula

G.f.: -(x^2-x-1)*(x^4+18*x^2+1) / (x^8-646*x^4+1). - Colin Barker, Nov 19 2013

a(n) = 646*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Dec 21 2013

Mathematica

Denominator[Convergents[Sqrt[322], 30]] (* Harvey P. Dale, Apr 25 2012 *)
CoefficientList[Series[-(x^2 - x - 1) (x^4 + 18 x^2 + 1)/(x^8 - 646 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 21 2013 *)

Prog

(Magma) I:=[1, 1, 17, 18, 629, 647, 10981, 11628]; [n le 8 select I[n] else 646*Self(n-4)-Self(n-8): n in [1..70]]; // Vincenzo Librandi, Dec 21 2013

Crossrefs

Cf. A041608, A040304.

Sequence in context: A197351 A041143 A041608 * A041610 A042399 A156656

Adjacent sequences: A041606 A041607 A041608 * A041610 A041611 A041612

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 19 2013

Status

approved