A041361 Denominators of continued fraction convergents to sqrt(194).

1, 1, 13, 14, 377, 391, 5069, 5460, 147029, 152489, 1976897, 2129386, 57340933, 59470319, 770984761, 830455080, 22362816841, 23193271921, 300682079893, 323875351814, 8721441227057, 9045316578871, 117265240173509, 126310556752380, 3401339715735389

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,390,0,0,0,-1).

Formula

G.f.: -(x^2-x-1)*(x^4+14*x^2+1) / (x^8-390*x^4+1). - Colin Barker, Nov 16 2013

a(n) = 390*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 16 2013

Mathematica

Denominator[Convergents[Sqrt[194], 30]] (* Vincenzo Librandi, Dec 16 2013 *)

Prog

(Magma) I:=[1, 1, 13, 14, 377, 391, 5069, 5460]; [n le 8 select I[n] else 390*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 16 2013

Crossrefs

Cf. A041360, A010236.

Sequence in context: A249313 A041083 A041360 * A041362 A041835 A042505

Adjacent sequences: A041358 A041359 A041360 * A041362 A041363 A041364

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 16 2013

Status

approved