A041647 Denominators of continued fraction convergents to sqrt(342).

1, 2, 73, 148, 5401, 10950, 399601, 810152, 29565073, 59940298, 2187415801, 4434771900, 161839204201, 328113180302, 11973913695073, 24275940570448, 885907774231201, 1796091489032850, 65545201379413801, 132886494247860452, 4849458994302390073

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,74,0,-1).

Formula

G.f.: -(x^2-2*x-1) / (x^4-74*x^2+1). - Colin Barker, Nov 20 2013

a(n) = 74*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Dec 22 2013

Mathematica

Denominator[Convergents[Sqrt[342], 30]] (* Harvey P. Dale, Oct 13 2012 *)
CoefficientList[Series[(1 + 2 x - x^2)/(x^4 - 74 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 22 2013 *)

Prog

(Magma) I:=[1, 2, 73, 148]; [n le 4 select I[n] else 74*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 22 2013

Crossrefs

Cf. A041646, A040323.

Sequence in context: A324566 A276518 A297410 * A345293 A083018 A240174

Adjacent sequences: A041644 A041645 A041646 * A041648 A041649 A041650

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 20 2013

Status

approved