A041269 Denominators of continued fraction convergents to sqrt(147).

1, 8, 193, 1552, 37441, 301080, 7263361, 58407968, 1409054593, 11330844712, 273349327681, 2198125466160, 53028360515521, 426425009590328, 10287228590683393, 82724253735057472, 1995669318232062721, 16048078799591559240, 387149560508429484481

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0, 194, 0, -1).

Formula

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

a(n) = 194*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 14 2013

Mathematica

Denominator[Convergents[Sqrt[147], 30]] (* Vincenzo Librandi, Dec 14 2013 *)

Prog

(Magma) I:=[1, 8, 193, 1552]; [n le 4 select I[n] else 194*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 14 2013

Crossrefs

Cf. A041268, A176910, A040132.

Sequence in context: A265269 A003956 A204820 * A172340 A103500 A232911

Adjacent sequences: A041266 A041267 A041268 * A041270 A041271 A041272

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 14 2013

Status

approved