A041663 Denominators of continued fraction convergents to sqrt(350).

1, 1, 3, 7, 17, 24, 881, 905, 2691, 6287, 15265, 21552, 791137, 812689, 2416515, 5645719, 13707953, 19353672, 710440145, 729793817, 2170027779, 5069849375, 12309726529, 17379575904, 637974459073, 655354034977, 1948682529027, 4552719093031, 11054120715089

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,898,0,0,0,0,0,-1).

Formula

G.f.: -(x^10-x^9+3*x^8-7*x^7+17*x^6-24*x^5-17*x^4-7*x^3-3*x^2-x-1) / ((x^6-30*x^3+1)*(x^6+30*x^3+1)). - Colin Barker, Nov 21 2013

a(n) = 898*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 22 2013

Mathematica

Denominator[Convergents[Sqrt[350], 30]] (* Vincenzo Librandi, Dec 22 2013 *)

Prog

(Magma) I:=[1, 1, 3, 7, 17, 24, 881, 905, 2691, 6287, 15265, 21552]; [n le 12 select I[n] else 898*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 22 2013

Crossrefs

Cf. A041662, A040331.

Sequence in context: A100343 A085396 A041077 * A042825 A076033 A029519

Adjacent sequences: A041660 A041661 A041662 * A041664 A041665 A041666

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 21 2013

Status

approved