A041639 Denominators of continued fraction convergents to sqrt(338).

1, 2, 3, 5, 13, 473, 959, 1432, 2391, 6214, 226095, 458404, 684499, 1142903, 2970305, 108073883, 219118071, 327191954, 546310025, 1419812004, 51659542169, 104738896342, 156398438511, 261137334853, 678673108217, 24693369230665, 50065411569547

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, 478, 0, 0, 0, 0, 1).

Formula

G.f.: -(x^8-2*x^7+3*x^6-5*x^5+13*x^4+5*x^3+3*x^2+2*x+1) / (x^10+478*x^5-1). - Colin Barker, Nov 20 2013

a(n) = 478*a(n-5) + a(n-10) for n>9. - Vincenzo Librandi, Dec 22 2013

Mathematica

Denominator[Convergents[Sqrt[338], 30]] (* Vincenzo Librandi, Dec 22 2013 *)

Prog

(Magma) I:=[1, 2, 3, 5, 13, 473, 959, 1432, 2391, 6214]; [n le 10 select I[n] else 478*Self(n-5)+Self(n-10): n in [1..40]]; // Vincenzo Librandi, Dec 22 2013

Crossrefs

Cf. A041638, A040319.

Sequence in context: A120494 A038601 A114747 * A006985 A042907 A115347

Adjacent sequences: A041636 A041637 A041638 * A041640 A041641 A041642

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 20 2013

Status

approved