A041157 Denominators of continued fraction convergents to sqrt(88).

1, 2, 3, 5, 8, 21, 386, 793, 1179, 1972, 3151, 8274, 152083, 312440, 464523, 776963, 1241486, 3259935, 59920316, 123100567, 183020883, 306121450, 489142333, 1284406116, 23608452421, 48501310958, 72109763379, 120611074337, 192720837716, 506052749769

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,394,0,0,0,0,0,-1).

Formula

a(n) = 394*a(n-6)-a(n-12). G.f.: -(x^10-2*x^9+3*x^8-5*x^7+8*x^6 -21*x^5 -8*x^4 -5*x^3-3*x^2-2*x-1) / (x^12-394*x^6+1). - Colin Barker, Jul 18 2012

Mathematica

Denominator/@Convergents[Sqrt[88], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *)
CoefficientList[Series[- (x^10 - 2 x^9 + 3 x^8 - 5 x^7 + 8 x^6 - 21 x^5 - 8 x^4 - 5 x^3 - 3 x^2 - 2 x - 1)/(x^12 - 394 x^6 + 1), {x, 0, 30}], x]  (* Vincenzo Librandi, Oct 24 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 394, 0, 0, 0, 0, 0, -1}, {1, 2, 3, 5, 8, 21, 386, 793, 1179, 1972, 3151, 8274}, 30] (* Harvey P. Dale, Jul 28 2017 *)

Crossrefs

Cf. A010539, A041156.

Sequence in context: A273046 A117774 A053056 * A178356 A042785 A136682

Adjacent sequences: A041154 A041155 A041156 * A041158 A041159 A041160

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved