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
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).
Programs
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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
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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
Comments