OFFSET
0,2
COMMENTS
From Johannes W. Meijer, Jun 12 2010: (Start)
The a(n) terms of this sequence can be constructed with the terms of sequence A099371.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,756,0,0,0,0,1).
FORMULA
From Johannes W. Meijer, Jun 12 2010: (Start)
a(5*n) = A099371(3*n+1), a(5*n+1) = (A099371(3*n+2)-A099371(3*n+1))/2, a(5*n+2) = (A099371(3*n+2)+A099371(3*n+1))/2, a(5*n+3):= A099371(3*n+2) and a(5*n+4) = A099371(3*n+3)/2. (End)
G.f.: -(x^8-4*x^7+5*x^6-9*x^5+41*x^4+9*x^3+5*x^2+4*x+1) / (x^10+756*x^5-1). - Colin Barker, Nov 11 2013
a(n) = 756*a(n-5) + a(n-10). - Vincenzo Librandi, Dec 12 2013
MATHEMATICA
Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[85], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Jun 23 2011 *)
Denominator[Convergents[Sqrt[85], 30]] (* Vincenzo Librandi, Dec 12 2013 *)
PROG
(Magma) I:=[1, 4, 5, 9, 41, 747, 3029, 3776, 6805, 30996]; [n le 10 select I[n] else 756*Self(n-5)+Self(n-10): n in [1..30]]; // Vincenzo Librandi, Dec 12 2013
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
STATUS
approved