A041412 Numerators of continued fraction convergents to sqrt(221).

14, 15, 104, 223, 1442, 1665, 48062, 49727, 346424, 742575, 4801874, 5544449, 160046446, 165590895, 1153591816, 2472774527, 15990238978, 18463013505, 532954617118, 551417630623, 3841460400856, 8234338432335, 53247490994866, 61481829427201, 1774738714956494

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,3330,0,0,0,0,0,-1).

Formula

G.f.: -(x^11 -14*x^10 +15*x^9 -104*x^8 +223*x^7 -1442*x^6 -1665*x^5 -1442*x^4 -223*x^3 -104*x^2 -15*x -14) / ((x^4 -15*x^2 +1)*(x^8 +15*x^6 +224*x^4 +15*x^2 +1)). - Colin Barker, Nov 07 2013

a(n) = 3330*a(n-6)-a(n-12). - Wesley Ivan Hurt, May 24 2021

Mathematica

Numerator[Convergents[Sqrt[221], 30]] (* Vincenzo Librandi, Nov 01 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 3330, 0, 0, 0, 0, 0, -1}, {14, 15, 104, 223, 1442, 1665, 48062, 49727, 346424, 742575, 4801874, 5544449}, 30] (* Harvey P. Dale, Jul 13 2024 *)

Crossrefs

Cf. A041413.

Sequence in context: A041406 A041410 A372335 * A041414 A033050 A225757

Adjacent sequences: A041409 A041410 A041411 * A041413 A041414 A041415

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 07 2013

Status

approved