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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A041581 Denominators of continued fraction convergents to sqrt(308). 2
1, 1, 2, 9, 11, 20, 691, 711, 1402, 6319, 7721, 14040, 485081, 499121, 984202, 4435929, 5420131, 9856060, 340526171, 350382231, 690908402, 3114015839, 3804924241, 6918940080, 239048886961, 245967827041, 485016714002, 2186034683049, 2671051397051 (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 (0,0,0,0,0,702,0,0,0,0,0,-1).

FORMULA

G.f.: -(x^4 -x^3 +2*x^2 +x +1)*(x^6 -10*x^3 -1) / ((x^4 -9*x^2 +1)*(x^8 +9*x^6 +80*x^4 +9*x^2 +1)). - Colin Barker, Nov 19 2013

a(n) = 702*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 20 2013

MATHEMATICA

Denominator[Convergents[Sqrt[308], 30]] (* Harvey P. Dale, Nov 25 2011 *)

CoefficientList[Series[-(x^4 - x^3 + 2 x^2 + x + 1) (x^6 - 10 x^3 - 1)/((x^4 - 9 x^2 + 1) (x^8 + 9 x^6 + 80 x^4 + 9 x^2 + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 20 2013 *)

PROG

(MAGMA) I:=[1, 1, 2, 9, 11, 20, 691, 711, 1402, 6319, 7721, 14040]; [n le 12 select I[n] else 702*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 20 2013

CROSSREFS

Cf. A041580, A040290.

Sequence in context: A131140 A022114 A041099 * A042463 A081613 A115911

Adjacent sequences:  A041578 A041579 A041580 * A041582 A041583 A041584

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 19 19:32 EDT 2019. Contains 321330 sequences. (Running on oeis4.)