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

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

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).

Crossrefs

Cf. A041413.

Programs

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 *)

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

Extensions

More terms from Colin Barker, Nov 07 2013