A041077 Denominators of continued fraction convergents to sqrt(45).

1, 1, 3, 7, 17, 24, 305, 329, 963, 2255, 5473, 7728, 98209, 105937, 310083, 726103, 1762289, 2488392, 31622993, 34111385, 99845763, 233802911, 567451585, 801254496, 10182505537, 10983760033, 32150025603, 75283811239, 182717648081, 258001459320, 3278735159921

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, A041076.

Programs

Mathematica

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[45],n]]],{n,1,50}] (* Vladimir Joseph Stephan Orlovsky, Mar 22 2011*)
Denominator[Convergents[Sqrt[45], 30]] (* Vincenzo Librandi, Oct 24 2013 *)
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 *)

Formula

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]

Extensions

More terms from Vincenzo Librandi, Oct 24 2013