A042019 Denominators of continued fraction convergents to sqrt(533).

1, 11, 12, 23, 265, 12213, 134608, 146821, 281429, 3242540, 149438269, 1647063499, 1796501768, 3443565267, 39675719705, 1828526671697, 20153469108372, 21981995780069, 42135464888441, 485472109552920, 22373852504322761, 246597849657103291, 268971702161426052

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, 12236, 0, 0, 0, 0, 1).

Formula

G.f.: -(x^8-11*x^7+12*x^6-23*x^5+265*x^4+23*x^3+12*x^2+11*x+1) / (x^10+12236*x^5-1). - Colin Barker, Nov 29 2013

a(n) = 12236*a(n-5) + a(n-10) for n>9. - Vincenzo Librandi, Jan 12 2014

Mathematica

Denominator[Convergents[Sqrt[533], 30]] (* Vincenzo Librandi, Jan 12 2014 *)

Prog

(Magma) I:=[1, 11, 12, 23, 265, 12213, 134608, 146821, 281429, 3242540]; [n le 10 select I[n] else 12236*Self(n-5)+Self(n-10): n in [1..30]]; // Vincenzo Librandi, Jan 12 2014

Crossrefs

Cf. A042018, A040509.

Sequence in context: A042615 A041244 A041242 * A221644 A022316 A368359

Adjacent sequences: A042016 A042017 A042018 * A042020 A042021 A042022

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 29 2013

Status

approved