A041351 Denominators of continued fraction convergents to sqrt(189).

1, 1, 3, 4, 107, 111, 329, 440, 11769, 12209, 36187, 48396, 1294483, 1342879, 3980241, 5323120, 142381361, 147704481, 437790323, 585494804, 15660655227, 16246150031, 48152955289, 64399105320, 1722529693609, 1786928798929, 5296387291467, 7083316090396

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,110,0,0,0,-1).

Formula

G.f.: -(x^2-x-1)*(x^4+4*x^2+1) / (x^8-110*x^4+1). - Colin Barker, Nov 16 2013

a(n) = 110*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 16 2013

Mathematica

Denominator[Convergents[Sqrt[189], 30]] (* Vincenzo Librandi, Dec 16 2013 *)

Prog

(Magma) I:=[1, 1, 3, 4, 107, 111, 329, 440]; [n le 8 select I[n] else 110*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 16 2013

Crossrefs

Cf. A041350, A010231.

Sequence in context: A156182 A126578 A332972 * A266516 A066496 A041465

Adjacent sequences: A041348 A041349 A041350 * A041352 A041353 A041354

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 16 2013

Status

approved