A042045 Denominators of continued fraction convergents to sqrt(546).

1, 2, 3, 8, 11, 30, 1391, 2812, 4203, 11218, 15421, 42060, 1950181, 3942422, 5892603, 15727628, 21620231, 58968090, 2734152371, 5527272832, 8261425203, 22050123238, 30311548441, 82673220120, 3833279673961, 7749232568042, 11582512242003, 30914257052048

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1402,0,0,0,0,0,-1).

Formula

G.f.: -(x^2-2*x-1)*(x^8+4*x^6+15*x^4+4*x^2+1) / (x^12-1402*x^6+1). - Colin Barker, Nov 30 2013

a(n) = 1402*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Jan 13 2014

Mathematica

Denominator[Convergents[Sqrt[546], 30]] (* Vincenzo Librandi, Jan 13 2014 *)

Prog

(Magma) I:=[1, 2, 3, 8, 11, 30, 1391, 2812, 4203, 11218, 15421, 42060]; [n le 12 select I[n] else 1402*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Jan 13 2014

Crossrefs

Cf. A042044, A040522.

Sequence in context: A239453 A143914 A041123 * A317912 A096506 A119155

Adjacent sequences: A042042 A042043 A042044 * A042046 A042047 A042048

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 30 2013

Status

approved