OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,394,0,0,0,0,0,-1).
FORMULA
From Colin Barker, Jul 16 2012: (Start)
a(n) = 394*a(n-6) - a(n-12).
G.f.: -(x^10 - x^9 + 3*x^8 - 13*x^7 + 29*x^6 - 42*x^5 - 29*x^4 - 13*x^3 - 3*x^2 - x - 1)/(x^12 - 394*x^6 + 1). (End)
MATHEMATICA
Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[22], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 17 2011 *)
LinearRecurrence[{0, 0, 0, 0, 0, 394, 0, 0, 0, 0, 0, -1 }, {1, 1, 3, 13, 29, 42, 365, 407, 1179, 5123, 11425, 16548}, 50] (* Stefano Spezia, Sep 30 2018 *)
CoefficientList[Series[-(x^10 - x^9 + 3*x^8 - 13*x^7 + 29*x^6 - 42*x^5 - 29*x^4 - 13*x^3 - 3*x^2 - x- 1)/(x^12 - 394*x^6 + 1), {x, 0, 50}], x] (* Stefano Spezia, Sep 30 2018 *)
PROG
(PARI) vector(26, i, contfracpnqn(contfrac(sqrt(22), i))[2, 1]) \\ Arkadiusz Wesolowski, Sep 29 2018
(PARI) Vec(-(x^10 - x^9 + 3*x^8 - 13*x^7 + 29*x^6 - 42*x^5 - 29*x^4 - 13*x^3 - 3*x^2 - x - 1)/(x^12 - 394*x^6 + 1) + O(x^50)) \\ Stefano Spezia, Sep 30 2018
CROSSREFS
KEYWORD
nonn,cofr,frac,easy
AUTHOR
STATUS
approved