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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A042075 Denominators of continued fraction convergents to sqrt(561). 2
1, 1, 3, 16, 19, 35, 89, 213, 515, 728, 1243, 6943, 15129, 22072, 1030441, 1052513, 3135467, 16729848, 19865315, 36595163, 93055641, 222706445, 538468531, 761174976, 1299643507, 7259392511, 15818428529, 23077821040, 1077398196369, 1100476017409 (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, 0, 0, 0, 0, 0, 0, 0, 0, 1045570, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

FORMULA

G.f.: -(x^26 -x^25 +3*x^24 -16*x^23 +19*x^22 -35*x^21 +89*x^20 -213*x^19 +515*x^18 -728*x^17 +1243*x^16 -6943*x^15 +15129*x^14 -22072*x^13 -15129*x^12 -6943*x^11 -1243*x^10 -728*x^9 -515*x^8 -213*x^7 -89*x^6 -35*x^5 -19*x^4 -16*x^3 -3*x^2 -x -1)/(x^28 -1045570*x^14 +1). - Vincenzo Librandi, Jan 14 2014

a(n) = 1045570*a(n-14) - a(n-28)for n>27. - Vincenzo Librandi, Jan 14 2014

MATHEMATICA

Denominator[Convergents[Sqrt[561], 30]] (* or *) CoefficientList[Series[-(x^26 - x^25 + 3 x^24 - 16 x^23 + 19 x^22 - 35 x^21 + 89 x^20 - 213 x^19 + 515 x^18 - 728 x^17 + 1243 x^16 - 6943 x^15 + 15129 x^14 - 22072 x^13 - 15129 x^12 - 6943 x^11 - 1243 x^10 - 728 x^9 - 515 x^8 - 213 x^7 - 89 x^6 - 35 x^5 - 19 x^4 - 16 x^3 - 3 x^2 - x - 1)/(x^28 - 1045570 x^14 + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Jan 14 2014 *)

LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1045570, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 1, 3, 16, 19, 35, 89, 213, 515, 728, 1243, 6943, 15129, 22072, 1030441, 1052513, 3135467, 16729848, 19865315, 36595163, 93055641, 222706445, 538468531, 761174976, 1299643507, 7259392511, 15818428529, 23077821040}, 30] (* Harvey P. Dale, Mar 01 2015 *)

CROSSREFS

Cf. A042074.

Sequence in context: A103655 A022126 A127006 * A042777 A041461 A277724

Adjacent sequences:  A042072 A042073 A042074 * A042076 A042077 A042078

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Vincenzo Librandi, Jan 14 2014

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 12:14 EDT 2019. Contains 321448 sequences. (Running on oeis4.)