login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A041413 Denominators of continued fraction convergents to sqrt(221). 2
1, 1, 7, 15, 97, 112, 3233, 3345, 23303, 49951, 323009, 372960, 10765889, 11138849, 77598983, 166336815, 1075619873, 1241956688, 35850407137, 37092363825, 258404590087, 553901543999, 3581813854081, 4135715398080, 119381845000321, 123517560398401 (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 (0,0,0,0,0,3330,0,0,0,0,0,-1).

FORMULA

G.f.: -(x^10 -x^9 +7*x^8 -15*x^7 +97*x^6 -112*x^5 -97*x^4 -15*x^3 -7*x^2 -x -1) / ((x^4 -15*x^2 +1)*(x^8 +15*x^6 +224*x^4 +15*x^2 +1)). - Colin Barker, Nov 17 2013

a(n) = 3330*a(n-6) - a(n-12). - Vincenzo Librandi, Dec 17 2013

MATHEMATICA

Denominator/@Convergents[Sqrt[221], 30]  (* Harvey P. Dale, Apr 02 2011 *)

CoefficientList[Series[-(x^10 - x^9 + 7 x^8 - 15 x^7 + 97 x^6 - 112 x^5 - 97 x^4 - 15 x^3 - 7 x^2 - x - 1)/((x^4 - 15 x^2 + 1) (x^8 + 15 x^6 + 224 x^4 + 15 x^2 + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 17 2013 *)

PROG

(MAGMA) I:=[1, 1, 7, 15, 97, 112, 3233, 3345, 23303, 49951, 323009, 372960]; [n le 12 select I[n] else 3330*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 17 2013

CROSSREFS

Cf. A041412, A040206, A177157.

Sequence in context: A219523 A177128 A177177 * A144536 A231399 A231466

Adjacent sequences:  A041410 A041411 A041412 * A041414 A041415 A041416

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Colin Barker, Nov 17 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 February 19 22:38 EST 2019. Contains 320328 sequences. (Running on oeis4.)