A041121 Denominators of continued fraction convergents to sqrt(69).

1, 3, 10, 13, 62, 75, 287, 936, 15263, 46725, 155438, 202163, 964090, 1166253, 4462849, 14554800, 237339649, 726573747, 2417060890, 3143634637, 14991599438, 18135234075, 69397301663, 226327139064, 3690631526687, 11298221719125, 37585296684062, 48883518403187

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,15550,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^14 -3*x^13 +10*x^12 -13*x^11 +62*x^10 -75*x^9 +287*x^8 -936*x^7 -287*x^6 -75*x^5 -62*x^4 -13*x^3 -10*x^2 -3*x -1) / (x^16 -15550*x^8 +1). - Colin Barker, Nov 13 2013

a(n) = 15550*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 11 2013

Mathematica

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[69], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Jun 26 2011 *)
Denominator[Convergents[Sqrt[69], 30]] (* Vincenzo Librandi, Dec 11 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 15550, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 3, 10, 13, 62, 75, 287, 936, 15263, 46725, 155438, 202163, 964090, 1166253, 4462849, 14554800}, 30] (* Harvey P. Dale, Oct 18 2015 *)

Prog

(Magma) I:=[1, 3, 10, 13, 62, 75, 287, 936, 15263, 46725, 155438, 202163, 964090, 1166253, 4462849, 14554800]; [n le 16 select I[n] else 15550*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013

Crossrefs

Cf. A041120, A010148, A020826, A010521.

Sequence in context: A275432 A041985 A081519 * A002354 A079943 A041865

Adjacent sequences: A041118 A041119 A041120 * A041122 A041123 A041124

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 13 2013

Status

approved