A041415 Denominators of continued fraction convergents to sqrt(222).

1, 1, 9, 10, 289, 299, 2681, 2980, 86121, 89101, 798929, 888030, 25663769, 26551799, 238078161, 264629960, 7647717041, 7912347001, 70946493049, 78858840050, 2278994014449, 2357852854499, 21141816850441, 23499669704940, 679132568588761, 702632238293701

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,298,0,0,0,-1).

Formula

G.f.: -(x^2-x-1)*(x^4+10*x^2+1) / (x^8-298*x^4+1). - Colin Barker, Nov 17 2013

a(n) = 298*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 17 2013

Mathematica

Denominator[Convergents[Sqrt[222], 30]] (* Vincenzo Librandi, Dec 17 2013 *)
LinearRecurrence[{0, 0, 0, 298, 0, 0, 0, -1}, {1, 1, 9, 10, 289, 299, 2681, 2980}, 30] (* Harvey P. Dale, Dec 30 2017 *)

Prog

(Magma) I:=[1, 1, 9, 10, 289, 299, 2681, 2980]; [n le 8 select I[n] else 298*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 17 2013

Crossrefs

Cf. A041414, A040207.

Sequence in context: A041178 A221201 A119159 * A103869 A041753 A042191

Adjacent sequences: A041412 A041413 A041414 * A041416 A041417 A041418

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 17 2013

Status

approved