A042269 Denominators of continued fraction convergents to sqrt(660).

1, 1, 3, 13, 29, 42, 2129, 2171, 6471, 28055, 62581, 90636, 4594381, 4685017, 13964415, 60542677, 135049769, 195592446, 9914672069, 10110264515, 30135201099, 130651068911, 291437338921, 422088407832, 21395857730521, 21817946138353, 65031750007227

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,2158,0,0,0,0,0,-1).

Formula

G.f.: -(x^10 -x^9 +3*x^8 -13*x^7 +29*x^6 -42*x^5 -29*x^4 -13*x^3 -3*x^2 -x -1) / ((x^4 -13*x^2 +1)*(x^8 +13*x^6 +168*x^4 +13*x^2 +1)). - Colin Barker, Dec 06 2013

a(n) = 2158*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Jan 19 2014

Maple

convert(sqrt(660), confrac, 30, cvgts): denom(cvgts); # Wesley Ivan Hurt, Dec 07 2013

Mathematica

Denominator/@Convergents[Sqrt[660], 30] (* Harvey P. Dale, Jul 15 2011 *)

Prog

(Magma) I:=[1, 1, 3, 13, 29, 42, 2129, 2171, 6471, 28055, 62581, 90636]; [n le 12 select I[n] else 2158*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Jan 19 2014

Crossrefs

Cf. A042268, A040634.

Sequence in context: A296776 A074498 A041035 * A049043 A031378 A144391

Adjacent sequences: A042266 A042267 A042268 * A042270 A042271 A042272

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 06 2013

Status

approved