A041691 Denominators of continued fraction convergents to sqrt(365).

1, 9, 10, 19, 181, 6897, 62254, 69151, 131405, 1251796, 47699653, 430548673, 478248326, 908796999, 8657421317, 329890807045, 2977674684722, 3307565491767, 6285240176489, 59874727080168, 2281524869222873, 20593598550086025, 22875123419308898

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, 6916, 0, 0, 0, 0, 1).

Formula

G.f.: -(x^8 -9*x^7 +10*x^6 -19*x^5 +181*x^4 +19*x^3 +10*x^2 +9*x +1) / (x^10 +6916*x^5 -1). - Colin Barker, Nov 22 2013

a(n) = 6916*a(n-5) + a(n-10) for n>9. - Vincenzo Librandi, Dec 23 2013

Mathematica

Denominator[Convergents[Sqrt[365], 30]] (* Vincenzo Librandi, Dec 23 2013 *)
LinearRecurrence[{0, 0, 0, 0, 6916, 0, 0, 0, 0, 1}, {1, 9, 10, 19, 181, 6897, 62254, 69151, 131405, 1251796}, 30] (* Harvey P. Dale, Jun 03 2019 *)

Prog

(Magma) I:=[1, 9, 10, 19, 181, 6897, 62254, 69151, 131405, 1251796]; [n le 10 select I[n] else 6916*Self(n-5)+Self(n-10): n in [1..40]]; // Vincenzo Librandi, Dec 23 2013

Crossrefs

Cf. A041690, A040345, A176980.

Sequence in context: A041164 A182396 A041162 * A300023 A022314 A178350

Adjacent sequences: A041688 A041689 A041690 * A041692 A041693 A041694

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 22 2013

Status

approved