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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A041163 Denominators of continued fraction convergents to sqrt(91). 2
1, 1, 2, 11, 13, 76, 89, 165, 3059, 3224, 6283, 34639, 40922, 239249, 280171, 519420, 9629731, 10149151, 19778882, 109043561, 128822443, 753155776, 881978219, 1635133995, 30314390129, 31949524124, 62263914253, 343269095389, 405533009642, 2370934143599 (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 (0,0,0,0,0,0,0,3148,0,0,0,0,0,0,0,-1).

FORMULA

G.f.: -(x^14 -x^13 +2*x^12 -11*x^11 +13*x^10 -76*x^9 +89*x^8 -165*x^7 -89*x^6 -76*x^5 -13*x^4 -11*x^3 -2*x^2 -x -1) / (x^16 -3148*x^8 +1). - Colin Barker, Nov 14 2013

a(n) = 3148*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 12 2013

MATHEMATICA

Denominator[Convergents[Sqrt[91], 30]] (* Bruno Berselli, Nov 14 2013 *)

CoefficientList[Series[-(x^14 - x^13 + 2 x^12 - 11 x^11 + 13 x^10 - 76 x^9 + 89 x^8 - 165 x^7 - 89 x^6 - 76 x^5 - 13 x^4 - 11 x^3 - 2 x^2 - x - 1)/(x^16 - 3148 x^8 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 12 2013 *)

PROG

(MAGMA) I:=[1, 1, 2, 11, 13, 76, 89, 165, 3059, 3224, 6283, 34639, 40922, 239249, 280171, 519420]; [n le 16 select I[n] else 3148*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 12 2013

CROSSREFS

Cf. A041162, A010162, A020848, A010542.

Sequence in context: A262832 A091021 A042563 * A073914 A266991 A041971

Adjacent sequences:  A041160 A041161 A041162 * A041164 A041165 A041166

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Colin Barker, Nov 14 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 December 9 08:20 EST 2019. Contains 329877 sequences. (Running on oeis4.)