A041753 Denominators of continued fraction convergents to sqrt(396).

1, 1, 9, 10, 389, 399, 3581, 3980, 154821, 158801, 1425229, 1584030, 61618369, 63202399, 567237561, 630439960, 24523956041, 25154396001, 225759124049, 250913520050, 9760472885949, 10011386405999, 89851564133941, 99862950539940, 3884643684651661

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,0,0,398,0,0,0,-1).

Formula

G.f.: -(x^2-x-1)*(x^4+10*x^2+1) / ((x^4-20*x^2+1)*(x^4+20*x^2+1)). - Colin Barker, Nov 23 2013

a(n) = 398*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Dec 24 2013

Mathematica

Denominator[Convergents[Sqrt[396], 30]] (* Vincenzo Librandi, Dec 24 2013 *)

Prog

(Magma) I:=[1, 1, 9, 10, 389, 399, 3581, 3980]; [n le 8 select I[n] else 398*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 24 2013

Crossrefs

Cf. A041752, A040376.

Sequence in context: A119159 A041415 A103869 * A042191 A042729 A156292

Adjacent sequences: A041750 A041751 A041752 * A041754 A041755 A041756

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 23 2013

Status

approved