A041511 Denominators of continued fraction convergents to sqrt(272).

1, 2, 65, 132, 4289, 8710, 283009, 574728, 18674305, 37923338, 1232221121, 2502365580, 81307919681, 165118204942, 5365090477825, 10895299160592, 354014663616769, 718924626394130, 23359602708228929, 47438130042851988, 1541379764079492545, 3130197658201837078

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,66,0,-1).

Formula

G.f.: -(x^2-2*x-1) / ((x^2-8*x-1)*(x^2+8*x-1)). - Colin Barker, Nov 18 2013

a(n) = 66*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Dec 19 2013

Mathematica

Denominator[Convergents[Sqrt[272], 30]] (* Vincenzo Librandi, Dec 19 2013 *)

Prog

(Magma) I:=[1, 2, 65, 132]; [n le 4 select I[n] else 66*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 19 2013

Crossrefs

Cf. A041510, A040255.

Sequence in context: A273498 A003358 A303376 * A156651 A342608 A294179

Adjacent sequences: A041508 A041509 A041510 * A041512 A041513 A041514

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 18 2013

Status

approved