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

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• easy

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).

Crossrefs

Cf. A041690, A040345, A176980.

Programs

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

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 *)

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

Extensions

More terms from Colin Barker, Nov 22 2013