login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Denominators of continued fraction convergents to sqrt(45).
3

%I #22 Jun 11 2022 09:41:08

%S 1,1,3,7,17,24,305,329,963,2255,5473,7728,98209,105937,310083,726103,

%T 1762289,2488392,31622993,34111385,99845763,233802911,567451585,

%U 801254496,10182505537,10983760033,32150025603,75283811239,182717648081,258001459320,3278735159921

%N Denominators of continued fraction convergents to sqrt(45).

%H Vincenzo Librandi, <a href="/A041077/b041077.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,322,0,0,0,0,0,-1).

%F a(n) = 322*a(n-6)-a(n-12). G.f.: -(x^10-x^9+3*x^8-7*x^7+17*x^6-24*x^5-17*x^4-7*x^3-3*x^2-x-1)/((x^2-3*x+1)*(x^2+3*x+1)*(x^4-3*x^3+8*x^2-3*x+1)*(x^4+3*x^3+8*x^2+3*x+1)). [_Colin Barker_, Jul 18 2012]

%t Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[45],n]]],{n,1,50}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 22 2011*)

%t Denominator[Convergents[Sqrt[45], 30]] (* _Vincenzo Librandi_, Oct 24 2013 *)

%t LinearRecurrence[{0,0,0,0,0,322,0,0,0,0,0,-1},{1,1,3,7,17,24,305,329,963,2255,5473,7728},40] (* _Harvey P. Dale_, Jun 11 2022 *)

%Y Cf. A010499, A041076.

%K nonn,cofr,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Vincenzo Librandi_, Oct 24 2013