A041667 Denominators of continued fraction convergents to sqrt(352).

1, 1, 4, 21, 193, 986, 3151, 4137, 152083, 156220, 620743, 3259935, 29960158, 153060725, 489142333, 642203058, 23608452421, 24250655479, 96360418858, 506052749769, 4650835166779, 23760228583664, 75931520917771, 99691749501435, 3664834502969431

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,155234,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^14 -x^13 +4*x^12 -21*x^11 +193*x^10 -986*x^9 +3151*x^8 -4137*x^7 -3151*x^6 -986*x^5 -193*x^4 -21*x^3 -4*x^2 -x -1) / ((x^8 -394*x^4 +1)*(x^8 +394*x^4 +1)). - Colin Barker, Nov 21 2013

a(n) = 155234*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 22 2013

Mathematica

Denominator[Convergents[Sqrt[352], 30]] (* Vincenzo Librandi, Dec 22 2013 *)

Prog

(Magma) I:=[1, 1, 4, 21, 193, 986, 3151, 4137, 152083, 156220, 620743, 3259935, 29960158, 153060725, 489142333, 642203058]; [n le 16 select I[n] else 155234*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 22 2013

Crossrefs

Cf. A041666, A040333.

Sequence in context: A065527 A267988 A360630 * A377828 A286883 A217144

Adjacent sequences: A041664 A041665 A041666 * A041668 A041669 A041670

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 21 2013

Status

approved