A041032 Numerators of continued fraction convergents to sqrt(21).

4, 5, 9, 23, 32, 55, 472, 527, 999, 2525, 3524, 6049, 51916, 57965, 109881, 277727, 387608, 665335, 5710288, 6375623, 12085911, 30547445, 42633356, 73180801, 628079764, 701260565, 1329340329, 3359941223

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,110,0,0,0,0,0,-1).

Crossrefs

Cf. A010477, A041033.

Programs

Mathematica

Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[21],n]]],{n,1,50}] (* Vladimir Joseph Stephan Orlovsky, Mar 17 2011 *)
Numerator[Convergents[Sqrt[21],50]] (* Harvey P. Dale, Apr 20 2012 *)

Formula

a(n) = 110*a(n-6)-a(n-12). G.f.: -(x^11 -4*x^10 +5*x^9 -9*x^8 +23*x^7 -32*x^6 -55*x^5 -32*x^4 -23*x^3 -9*x^2 -5*x -4)/((x^4 -5*x^2 +1) *(x^8 +5*x^6 +24*x^4 +5*x^2 +1)). - Colin Barker, Jul 16 2012