A041337 Denominators of continued fraction convergents to sqrt(182).

1, 2, 53, 108, 2861, 5830, 154441, 314712, 8336953, 16988618, 450041021, 917070660, 24293878181, 49504827022, 1311419380753, 2672343588528, 70792352682481, 144257048953490, 3821475625473221, 7787208299899932, 206288891422871453, 420364991145642838

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,54,0,-1).

Formula

G.f.: -(x^2-2*x-1) / (x^4-54*x^2+1). - Colin Barker, Nov 15 2013

a(n) = 54*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 15 2013

Mathematica

Denominator[Convergents[Sqrt[182], 30]] (* Harvey P. Dale, Jun 21 2013 *)
CoefficientList[Series[(1 + 2 x - x^2)/(x^4 - 54 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 15 2013 *)

Prog

(Magma) I:=[1, 2, 53, 108]; [n le 4 select I[n] else 54*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 15 2013

Crossrefs

Cf. A041336, A040168.

Sequence in context: A062853 A059703 A212889 * A139844 A249657 A249658

Adjacent sequences: A041334 A041335 A041336 * A041338 A041339 A041340

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 15 2013

Status

approved