OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (0,14,0,-1).
FORMULA
From Colin Barker, Apr 14 2012: (Start)
a(n) = 14*a(n-2) - a(n-4).
G.f.: x*(1 + 6*x - x^2)/((1 - 4*x + x^2)*(1 + 4*x + x^2)). (End)
a(n) = ((-(-2-sqrt(3))^n*(-3+sqrt(3)) + (2-sqrt(3))^n*(-3+sqrt(3)) - (3+sqrt(3))*((-2+sqrt(3))^n - (2+sqrt(3))^n)))/(8*sqrt(3)). - Colin Barker, Mar 27 2016
EXAMPLE
0, 1, 6/7, 13/15, 84/97, 181/209, 1170/1351, 2521/2911, 16296/18817, 35113/40545, ...
MAPLE
with(numtheory); Digits:=200: cf:=convert(evalf(sqrt(3)/2, confrac); [seq(nthconver(cf, i), i=0..100)];
MATHEMATICA
CoefficientList[Series[x (1 + 6 x - x^2)/((1 - 4 x + x^2) (1 + 4 x + x^2)), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 10 2013 *)
Numerator[Convergents[Sqrt[3]/2, 30]] (* or *) LinearRecurrence[{0, 14, 0, -1}, {0, 1, 6, 13}, 30] (* Harvey P. Dale, Feb 10 2014 *)
PROG
(Magma) I:=[0, 1, 6, 13]; [n le 4 select I[n] else 14*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 10 2013
(PARI) Vec(x*(1+6*x-x^2)/((1-4*x+x^2)*(1+4*x+x^2)) + O(x^30)) \\ Colin Barker, Mar 27 2016
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
N. J. A. Sloane, Dec 29 2008
STATUS
approved