OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,8010,0,0,0,0,0,0,0,0,1).
FORMULA
G.f.: -(x^16 -3*x^15 +7*x^14 -10*x^13 +17*x^12 -27*x^11 +44*x^10 -115*x^9 +389*x^8 +115*x^7 +44*x^6 +27*x^5 +17*x^4 +10*x^3 +7*x^2 +3*x +1) / (x^18 +8010*x^9 -1). - Colin Barker, Nov 14 2013
a(n) = 8010*a(n-9) + a(n-18). - Vincenzo Librandi, Dec 12 2013
MATHEMATICA
Denominator[Convergents[Sqrt[106], 30]] (* Vincenzo Librandi, Dec 12 2013 *)
PROG
(Magma) I:=[1, 3, 7, 10, 17, 27, 44, 115, 389, 7895, 24074, 56043, 80117, 136160, 216277, 352437, 921151, 3115890]; [n le 18 select I[n] else 8010*Self(n-9)+Self(n-18): n in [1..40]]; // Vincenzo Librandi, Dec 12 2013
(Python)
from sympy import sqrt
from sympy.ntheory.continued_fraction import *
def aupton(terms):
g = continued_fraction_convergents(continued_fraction_iterator(sqrt(106)))
return [next(g).denominator() for n in range(terms)]
print(aupton(30)) # Michael S. Branicky, Oct 31 2021
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 14 2013
STATUS
approved