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

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• easy

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).

Crossrefs

Cf. A041268, A176910, A040132.

Programs

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

Mathematica

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

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

Extensions

More terms from Colin Barker, Nov 14 2013