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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A041557 Denominators of continued fraction convergents to sqrt(296). 2
1, 4, 5, 39, 44, 215, 7354, 29631, 36985, 288526, 325511, 1590570, 54404891, 219210134, 273615025, 2134515309, 2408130334, 11767036645, 402487376264, 1621716541701, 2024203917965, 15791143967456, 17815347885421, 87052535509140, 2977601555196181 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,7398,0,0,0,0,0,-1).

FORMULA

G.f.: -(x^10 -4*x^9 +5*x^8 -39*x^7 +44*x^6 -215*x^5 -44*x^4 -39*x^3 -5*x^2 -4*x -1) / ((x^6 -86*x^3 -1)*(x^6 +86*x^3 -1)). - Colin Barker, Nov 19 2013

a(n) = 7398*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 20 2013

MATHEMATICA

Denominator[Convergents[Sqrt[296], 40]] (* Harvey P. Dale, Jan 13 2012 *)

CoefficientList[Series[-(x^10 - 4 x^9 + 5 x^8 - 39 x^7 + 44 x^6 - 215 x^5 - 44 x^4 - 39 x^3 - 5 x^2 - 4 x - 1)/((x^6 - 86 x^3 - 1) (x^6 + 86 x^3 - 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 20 2013 *)

PROG

(MAGMA) I:=[1, 4, 5, 39, 44, 215, 7354, 29631, 36985, 288526, 325511, 1590570]; [n le 12 select I[n] else 7398*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 20 2013

CROSSREFS

Cf. A041556, A040278.

Sequence in context: A131139 A152291 A228798 * A270087 A265689 A270098

Adjacent sequences:  A041554 A041555 A041556 * A041558 A041559 A041560

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Colin Barker, Nov 19 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 March 24 14:04 EDT 2019. Contains 321448 sequences. (Running on oeis4.)