login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A041281 Denominators of continued fraction convergents to sqrt(153). 2
1, 2, 3, 8, 19, 46, 65, 176, 4289, 8754, 13043, 34840, 82723, 200286, 283009, 766304, 18674305, 38114914, 56789219, 151693352, 360175923, 872045198, 1232221121, 3336487440, 81307919681, 165952326802, 247260246483, 660472819768, 1568205886019, 3796884591806 (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 (0,0,0,0,0,0,0,4354,0,0,0,0,0,0,0,-1).

FORMULA

G.f.: -(x^2-2*x-1)*(x^4+4*x^2+1)*(x^8+22*x^4+1) / ((x^4-8*x^2-1)*(x^4+8*x^2-1)*(x^8+66*x^4+1)). - Colin Barker, Nov 14 2013

a(n) = 4354*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 14 2013

MATHEMATICA

Denominator[Convergents[Sqrt[153], 30]] (* Harvey P. Dale, Mar 04 2013 *)

CoefficientList[Series[-(x^2 - 2 x - 1) (x^4 + 4 x^2 + 1) (x^8 + 22 x^4 + 1)/((x^4 - 8 x^2 - 1) (x^4 + 8 x^2 - 1) (x^8 + 66 x^4 + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 14 2013 *)

PROG

(MAGMA) I:=[1, 2, 3, 8, 19, 46, 65, 176, 4289, 8754, 13043, 34840, 82723, 200286, 283009, 766304]; [n le 16 select I[n] else 4354*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 14 2013

CROSSREFS

Cf. A041280, A010204.

Sequence in context: A002356 A166302 A100342 * A078343 A148038 A326301

Adjacent sequences:  A041278 A041279 A041280 * A041282 A041283 A041284

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 August 14 04:13 EDT 2020. Contains 336477 sequences. (Running on oeis4.)