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A041033 Denominators of continued fraction convergents to sqrt(21). 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 23 08:38 EDT 2022. Contains 353961 sequences. (Running on oeis4.)