A041193 Denominators of continued fraction convergents to sqrt(107).

1, 2, 3, 29, 32, 93, 1892, 3877, 5769, 55798, 61567, 178932, 3640207, 7459346, 11099553, 107355323, 118454876, 344265075, 7003756376, 14351777827, 21355534203, 206551585654, 227907119857, 662365825368

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1924,0,0,0,0,0,-1).

Crossrefs

Cf. A041192 (numerators), A010173 (continued fraction), A177935 (decimal expansion).

Programs

Mathematica

Denominator[Convergents[Sqrt[107],30]] (* or *) LinearRecurrence[ {0,0,0,0,0,1924,0,0,0,0,0,-1},{1,2,3,29,32,93,1892,3877,5769,55798,61567,178932},30] (* Harvey P. Dale, Aug 30 2013 *)
CoefficientList[Series[- (x^10 - 2 x^9 + 3 x^8 - 29 x^7 + 32 x^6 - 93 x^5 - 32 x^4 - 29 x^3 - 3 x^2 - 2 x - 1)/(x^12 - 1924 x^6 + 1), {x, 0, 30}], x]  (* Vincenzo Librandi, Oct 24 2013 *)

Formula

a(n) = 1924*a(n-6)-a(n-12). G.f.: -(x^10-2*x^9+3*x^8-29*x^7+32*x^6 -93*x^5 -32*x^4-29*x^3-3*x^2-2*x-1) / (x^12-1924*x^6+1). - Colin Barker, Jul 19 2012