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!)
A041537 Denominators of continued fraction convergents to sqrt(285). 2
1, 1, 8, 17, 127, 144, 4735, 4879, 38888, 82655, 617473, 700128, 23021569, 23721697, 189073448, 401868593, 3002153599, 3404022192, 111930863743, 115334885935, 919275065288, 1953885016511, 14596470180865, 16550355197376, 544207836496897, 560758191694273 (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, 4862, 0, 0, 0, 0, 0, -1).

FORMULA

G.f.: -(x^10 -x^9 +8*x^8 -17*x^7 +127*x^6 -144*x^5 -127*x^4 -17*x^3 -8*x^2 -x -1) / ((x^4 -17*x^2 +1)*(x^8 +17*x^6 +288*x^4 +17*x^2 +1)). - Colin Barker, Nov 18 2013

a(n) = 4862*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 19 2013

MATHEMATICA

Denominator[Convergents[Sqrt[285], 30]] (* Harvey P. Dale, Nov 08 2013 *)

CoefficientList[Series[-(x^10 - x^9 + 8 x^8 - 17 x^7 + 127 x^6 - 144 x^5 - 127 x^4 - 17 x^3 - 8 x^2 - x - 1)/((x^4 - 17 x^2 + 1) (x^8 + 17 x^6 + 288 x^4 + 17 x^2 + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 19 2013 *)

PROG

(MAGMA) I:=[1, 1, 8, 17, 127, 144, 4735, 4879, 38888, 82655, 617473, 700128]; [n le 12 select I[n] else 4862*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 19 2013

CROSSREFS

Cf. A041536, A176104, A040268.

Sequence in context: A097405 A192282 A088588 * A153315 A041126 A248289

Adjacent sequences:  A041534 A041535 A041536 * A041538 A041539 A041540

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Colin Barker, Nov 18 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 8 12:07 EST 2019. Contains 329862 sequences. (Running on oeis4.)