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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A041859 Denominators of continued fraction convergents to sqrt(451). 2
1, 4, 17, 38, 321, 6779, 54553, 115885, 518093, 2188257, 92424887, 371887805, 1579976107, 3531840019, 29834696259, 630060461458, 5070318387923, 10770697237304, 48153107337139, 203383126585860, 8590244423943259, 34564360822358896, 146847687713378843 (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, 0, 0, 0, 0, 92942980, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

FORMULA

G.f.: -(x^18 -4*x^17 +17*x^16 -38*x^15 +321*x^14 -6779*x^13 +54553*x^12 -115885*x^11 +518093*x^10 -2188257*x^9 -518093*x^8 -115885*x^7 -54553*x^6 -6779*x^5 -321*x^4 -38*x^3 -17*x^2 -4*x -1)/(x^20 -92942980*x^10 +1). - Vincenzo Librandi, Dec 26 2013

a(n) = 92942980*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Dec 26 2013

MATHEMATICA

Denominator[Convergents[Sqrt[451], 30]] (* or *) CoefficientList[Series[-(x^18 - 4 x^17 + 17 x^16 - 38 x^15 + 321 x^14 - 6779 x^13 + 54553 x^12 - 115885 x^11 + 518093 x^10 - 2188257 x^9 - 518093 x^8 - 115885 x^7 - 54553 x^6 - 6779 x^5 - 321 x^4 - 38 x^3 - 17 x^2 - 4 x - 1)/(x^20 - 92942980 x^10 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 26 2013 *)

PROG

(MAGMA) I:=[1, 4, 17, 38, 321, 6779, 54553, 115885, 518093, 2188257, 92424887, 371887805, 1579976107, 3531840019, 29834696259, 630060461458, 5070318387923, 10770697237304, 48153107337139, 203383126585860]; [n le 20 select I[n] else 92942980*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 26 2013

CROSSREFS

Cf. A041858.

Sequence in context: A218925 A182868 A178947 * A022266 A273309 A145995

Adjacent sequences:  A041856 A041857 A041858 * A041860 A041861 A041862

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Vincenzo Librandi, Dec 26 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 November 15 13:56 EST 2019. Contains 329149 sequences. (Running on oeis4.)