A041357 Denominators of continued fraction convergents to sqrt(192).

1, 1, 6, 7, 188, 195, 1163, 1358, 36471, 37829, 225616, 263445, 7075186, 7338631, 43768341, 51106972, 1372549613, 1423656585, 8490832538, 9914489123, 266267549736, 276182038859, 1647177744031, 1923359782890, 51654532099171, 53577891882061

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,0,0,194,0,0,0,-1).

Formula

G.f.: -(x^2-x-1)*(x^4+7*x^2+1) / ((x^2-4*x+1)*(x^2+4*x+1)*(x^4+14*x^2+1)). - Colin Barker, Nov 16 2013

a(n) = 194*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 16 2013

Mathematica

Denominator[Convergents[Sqrt[192], 30]] (* Harvey P. Dale, Oct 22 2013 *)
CoefficientList[Series[-(x^2 - x - 1) (x^4 + 7 x^2 + 1)/((x^2 - 4 x + 1) (x^2 + 4 x + 1) (x^4 + 14 x^2 + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 16 2013 *)

Prog

(Magma) I:=[1, 1, 6, 7, 188, 195, 1163, 1358]; [n le 8 select I[n] else 194*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 16 2013

Crossrefs

Cf. A041356, A010234, A200243.

Sequence in context: A041082 A036417 A267255 * A041829 A042497 A011315

Adjacent sequences: A041354 A041355 A041356 * A041358 A041359 A041360

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 16 2013

Status

approved