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

0,3

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).

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

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 *)

Prog

(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

Crossrefs

Cf. A041832, A040416.

Sequence in context: A177131 A177180 A275248 * A153317 A110418 A336759

Adjacent sequences: A041830 A041831 A041832 * A041834 A041835 A041836

Keyword

nonn,easy,frac

Author

N. J. A. Sloane.

Status

approved