login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A042269 Denominators of continued fraction convergents to sqrt(660). 2
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 19 22:05 EDT 2021. Contains 348095 sequences. (Running on oeis4.)