A041571 Denominators of continued fraction convergents to sqrt(303).

1, 2, 5, 27, 59, 145, 4989, 10123, 25235, 136298, 297831, 731960, 25184471, 51100902, 127386275, 688032277, 1503450829, 3694933935, 127131204619, 257957343173, 643045890965, 3473186797998, 7589419486961, 18652025771920, 641758295732241, 1302168617236402

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,5048,0,0,0,0,0,-1).

Formula

G.f.: -(x^4-2*x^3+5*x^2+2*x+1)*(x^6-29*x^3-1) / (x^12-5048*x^6+1). - Colin Barker, Nov 19 2013

a(n) = 5048*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 20 2013

Mathematica

Denominator[Convergents[Sqrt[303], 30]] (* Vincenzo Librandi, Dec 20 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 5048, 0, 0, 0, 0, 0, -1}, {1, 2, 5, 27, 59, 145, 4989, 10123, 25235, 136298, 297831, 731960}, 30] (* Harvey P. Dale, Mar 24 2023 *)

Prog

(Magma) I:=[1, 2, 5, 27, 59, 145, 4989, 10123, 25235, 136298, 297831, 731960]; [n le 12 select I[n] else 5048*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 20 2013

Crossrefs

Cf. A041570, A040285.

Sequence in context: A138613 A299104 A090744 * A042259 A100105 A087130

Adjacent sequences: A041568 A041569 A041570 * A041572 A041573 A041574

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 19 2013

Status

approved