A041076 Numerators of continued fraction convergents to sqrt(45).

6, 7, 20, 47, 114, 161, 2046, 2207, 6460, 15127, 36714, 51841, 658806, 710647, 2080100, 4870847, 11821794, 16692641, 212133486, 228826127, 669785740, 1568397607, 3806580954, 5374978561, 68306323686

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 (0,0,0,0,0,322,0,0,0,0,0,-1).

Crossrefs

Cf. A010499, A041077.

Programs

Mathematica

Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[45],n]]],{n,1,50}] (* Vladimir Joseph Stephan Orlovsky, Mar 22 2011*)
Numerator[Convergents[Sqrt[45], 30]] (* Vincenzo Librandi, Oct 25 2013 *)

Formula

a(n) = 322*a(n-6)-a(n-12). G.f.: -(x^11-6*x^10+7*x^9-20*x^8+47*x^7-114*x^6-161*x^5-114*x^4-47*x^3-20*x^2-7*x-6)/((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]