A041833 Denominators of continued fraction convergents to sqrt(437).

1, 1, 10, 21, 199, 220, 8999, 9219, 91970, 193159, 1830401, 2023560, 82772801, 84796361, 845940050, 1776676461, 16836028199, 18612704660, 761344214599, 779956919259, 7780956487930, 16341869895119, 154857785544001, 171199655439120, 7002844003108801

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• frac

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, 9198, 0, 0, 0, 0, 0, -1).

Crossrefs

Cf. A041832, A040416.

Programs

Magma

I:=[1,1,10,21,199,220,8999,9219,91970,193159, 1830401,2023560]; [n le 12 select I[n] else 9198*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 25 2013

Mathematica

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[437], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Jun 23 2011 *)
Denominator[Convergents[Sqrt[437], 30]] (* Vincenzo Librandi, Dec 25 2013 *)

Formula

G.f.: -(x^10 -x^9 +10*x^8 -21*x^7 +199*x^6 -220*x^5 -199*x^4 -21*x^3 -10*x^2 -x -1) / ((x^4 -21*x^2 +1)*(x^8 +21*x^6 +440*x^4 +21*x^2 +1)). - Colin Barker, Nov 25 2013

a(n) = 9198*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 25 2013