A041339 Denominators of continued fraction convergents to sqrt(183).

1, 1, 2, 17, 19, 36, 955, 991, 1946, 16559, 18505, 35064, 930169, 965233, 1895402, 16128449, 18023851, 34152300, 905983651, 940135951, 1846119602, 15709092767, 17555212369, 33264305136, 882427145905, 915691451041, 1798118596946, 15300640226609

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,974,0,0,0,0,0,-1).

Formula

G.f.: -(x^4-x^3+2*x^2+x+1)*(x^6-18*x^3-1) / (x^12-974*x^6+1). - Colin Barker, Nov 15 2013

a(n) = 974*a(n-6) - a(n-12). - Vincenzo Librandi, Dec 16 2013

Mathematica

Denominator[Convergents[Sqrt[183], 30]] (* Vincenzo Librandi, Dec 16 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 974, 0, 0, 0, 0, 0, -1}, {1, 1, 2, 17, 19, 36, 955, 991, 1946, 16559, 18505, 35064}, 30] (* Harvey P. Dale, Dec 12 2024 *)

Prog

(Magma) I:=[1, 1, 2, 17, 19, 36, 955, 991, 1946, 16559, 18505, 35064]; [n le 12 select I[n] else 974*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 16 2013

Crossrefs

Cf. A041338, A010226.

Sequence in context: A043297 A018569 A022118 * A042925 A019413 A040138

Adjacent sequences: A041336 A041337 A041338 * A041340 A041341 A041342

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 15 2013

Status

approved