A042303 Denominators of continued fraction convergents to sqrt(678).

1, 26, 1353, 35204, 1831961, 47666190, 2480473841, 64539986056, 3358559748753, 87387093453634, 4547487419337721, 118322059996234380, 6157294607223525481, 160207981847807896886, 8336972350693234163553, 216921489099871896149264

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,1354,0,-1).

Formula

G.f.: -(x^2-26*x-1) / (x^4-1354*x^2+1). - Colin Barker, Dec 07 2013

a(n) = 1354*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Jan 19 2014

Mathematica

Denominator[Convergents[Sqrt[678], 30]] (* Vincenzo Librandi, Jan 19 2014 *)

Prog

(Magma) I:=[1, 26, 1353, 35204]; [n le 4 select I[n] else 1354*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jan 19 2014

Crossrefs

Cf. A042302, A040651.

Sequence in context: A220955 A106710 A114052 * A042300 A282884 A080163

Adjacent sequences: A042300 A042301 A042302 * A042304 A042305 A042306

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 07 2013

Status

approved