A041033 Denominators of continued fraction convergents to sqrt(21).

1, 1, 2, 5, 7, 12, 103, 115, 218, 551, 769, 1320, 11329, 12649, 23978, 60605, 84583, 145188, 1246087, 1391275, 2637362, 6665999, 9303361, 15969360, 137058241, 153027601, 290085842, 733199285, 1023285127

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,110,0,0,0,0,0,-1).

Formula

a(n) = 110*a(n-6)-a(n-12). G.f.: -(x^4-x^3+2*x^2+x+1)*(x^6-6*x^3-1)/((x^4-5*x^2+1)*(x^8+5*x^6+24*x^4+5*x^2+1)). [Colin Barker, Jul 16 2012]

Mathematica

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[21], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 17 2011 *)
Denominator[Convergents[Sqrt[21], 30]] (* Harvey P. Dale, Apr 22 2013 *)
CoefficientList[Series[- (x^4 - x^3 + 2 x^2 + x + 1) (x^6 - 6 x^3 - 1)/((x^4 - 5 x^2 + 1) (x^8 + 5 x^6 + 24 x^4 + 5 x^2 + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 22 2013 *)

Crossrefs

Cf. A010477, A041032.

Sequence in context: A071013 A114727 A295334 * A134472 A041203 A041517

Adjacent sequences: A041030 A041031 A041032 * A041034 A041035 A041036

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved