A042925 Denominators of continued fraction convergents to sqrt(994).

1, 1, 2, 17, 19, 36, 2251, 2287, 4538, 38591, 43129, 81720, 5109769, 5191489, 10301258, 87601553, 97902811, 185504364, 11599173379, 11784677743, 23383851122, 198855486719, 222239337841, 421094824560, 26330118460561, 26751213285121, 53081331745682

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, 2270, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^4 - x^3 + 2*x^2 + x + 1)*(x^6 - 18*x^3 - 1) / (x^12 - 2270*x^6 + 1). - Colin Barker, Dec 25 2013

a(n) = 2270*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Feb 01 2014

Mathematica

Denominator[Convergents[Sqrt[994], 30]] (* Vincenzo Librandi, Feb 01 2014 *)
LinearRecurrence[{0, 0, 0, 0, 0, 2270, 0, 0, 0, 0, 0, -1}, {1, 1, 2, 17, 19, 36, 2251, 2287, 4538, 38591, 43129, 81720}, 30] (* Harvey P. Dale, Oct 27 2018 *)

Prog

(Magma) I:=[1, 1, 2, 17, 19, 36, 2251, 2287, 4538, 38591, 43129, 81720]; [n le 12 select I[n] else 2270*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Feb 01 2014

Crossrefs

Cf. A042924, A040962.

Sequence in context: A018569 A022118 A041339 * A019413 A040138 A240475

Adjacent sequences: A042922 A042923 A042924 * A042926 A042927 A042928

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Dec 25 2013

Status

approved