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A041189
Denominators of continued fraction convergents to sqrt(105).
2
1, 4, 81, 328, 6641, 26892, 544481, 2204816, 44640801, 180768020, 3660001201, 14820772824, 300075457681, 1215122603548, 24602527528641, 99625232718112, 2017107181890881, 8168053960281636, 165378186387523601, 669680799510376040
OFFSET
0,2
FORMULA
G.f.: (1 + 4*x - x^2)/(1 - 82*x^2 + x^4). - Vincenzo Librandi, Dec 12 2013
a(n) = 82*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 12 2013
MATHEMATICA
Denominator/@Convergents[Sqrt[105], 30] (* Harvey P. Dale, Apr 02 2011 *)
CoefficientList[Series[(1 + 4 x - x^2)/(1 - 82 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 12 2013*)
PROG
(Magma) I:=[1, 4, 81, 328]; [n le 4 select I[n] else 82*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 12 2013
CROSSREFS
Cf. A040094, A041188 (numerators), A176461.
Sequence in context: A272884 A053901 A017006 * A123198 A202831 A335691
KEYWORD
nonn,frac,easy
EXTENSIONS
a(19) from Vincenzo Librandi, Dec 12 2013
STATUS
approved