login
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
OFFSET
0,3
LINKS
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
Sequence in context: A071013 A114727 A295334 * A134472 A041203 A041517
KEYWORD
nonn,cofr,frac,easy
AUTHOR
STATUS
approved