A041991 Denominators of continued fraction convergents to sqrt(518).

1, 1, 4, 25, 79, 104, 4655, 4759, 18932, 118351, 373985, 492336, 22036769, 22529105, 89624084, 560273609, 1770444911, 2330718520, 104322059791, 106652778311, 424280394724, 2652335146655, 8381285834689, 11033620981344, 493860609013825, 504894229995169

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, 0, 0, 4734, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^10-x^9+4*x^8-25*x^7+79*x^6-104*x^5-79*x^4-25*x^3-4*x^2-x-1) / (x^12-4734*x^6+1). - Colin Barker, Nov 28 2013

a(n) = 4734*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Jan 11 2014

Mathematica

Denominator[Convergents[Sqrt[518], 30]] (* Harvey P. Dale, Jan 21 2013 *)
CoefficientList[Series[-(x^10 - x^9 + 4 x^8 - 25 x^7 + 79 x^6 - 104 x^5 - 79 x^4 - 25 x^3 - 4 x^2 - x - 1)/(x^12 - 4734 x^6 + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Jan 11 2014 *)

Prog

(Magma) I:=[1, 1, 4, 25, 79, 104, 4655, 4759, 18932, 118351, 373985, 492336]; [n le 12 select I[n] else 4734*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Jan 11 2014

Crossrefs

Cf. A041990, A040495.

Sequence in context: A273361 A266126 A303514 * A027764 A095669 A323967

Adjacent sequences: A041988 A041989 A041990 * A041992 A041993 A041994

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 28 2013

Status

approved