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A041357 Denominators of continued fraction convergents to sqrt(192). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 26 01:48 EST 2020. Contains 331270 sequences. (Running on oeis4.)