A041333 Denominators of continued fraction convergents to sqrt(180).

1, 2, 5, 12, 317, 646, 1609, 3864, 102073, 208010, 518093, 1244196, 32867189, 66978574, 166824337, 400627248, 10583132785, 21566892818, 53716918421, 129000729660, 3407735889581, 6944472508822, 17296680907225, 41537834323272, 1097280373312297

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,322,0,0,0,-1).

Formula

G.f.: -(x^2-2*x-1)*(x^4+6*x^2+1) / ((x^2-4*x-1)*(x^2+4*x-1)*(x^4+18*x^2+1)). - Colin Barker, Nov 15 2013

a(n) = 322*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 15 2013

Mathematica

Denominator[Convergents[Sqrt[180], 30]] (* Vincenzo Librandi, Dec 15 2013 *)
LinearRecurrence[{0, 0, 0, 322, 0, 0, 0, -1}, {1, 2, 5, 12, 317, 646, 1609, 3864}, 30] (* Harvey P. Dale, May 07 2016 *)

Prog

(Magma) I:=[1, 2, 5, 12, 317, 646, 1609, 3864]; [n le 8 select I[n] else 322*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 15 2013

Crossrefs

Cf. A041332, A040166.

Sequence in context: A205082 A060807 A041095 * A197950 A041715 A042241

Adjacent sequences: A041330 A041331 A041332 * A041334 A041335 A041336

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 15 2013

Status

approved