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!)
A042298 Numerators of continued fraction convergents to sqrt(675). 2
25, 26, 1325, 1351, 68875, 70226, 3580175, 3650401, 186100225, 189750626, 9673631525, 9863382151, 502842739075, 512706121226, 26138148800375, 26650854921601, 1358680894880425, 1385331749802026, 70625268384981725, 72010600134783751, 3671155275124169275 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,52,0,-1).

FORMULA

G.f.: -(x^3-25*x^2-26*x-25) / (x^4-52*x^2+1). - Vincenzo Librandi, Nov 21 2013, simplified by Colin Barker, Dec 28 2013

a(n) = 52*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 21 2013, simplified by Colin Barker, Dec 28 2013

MATHEMATICA

Numerator[Convergents[Sqrt[675], 30]] (* or *) CoefficientList[Series[(25 + 26 x + 1325 x^2 + 1351 x^3 + 1325 x^4 - 26 x^5 + 25 x^6 - x^7)/(1 - 2702 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 21 2013 *)

PROG

(MAGMA) I:=[25, 26, 1325, 1351, 68875, 70226, 3580175, 3650401]; [n le 8 select I[n] else 2702*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 21 2013

CROSSREFS

Cf. A042299, A040649.

Sequence in context: A041311 A042296 A042297 * A157091 A070662 A183982

Adjacent sequences:  A042295 A042296 A042297 * A042299 A042300 A042301

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Colin Barker, Dec 28 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 May 18 07:26 EDT 2021. Contains 343995 sequences. (Running on oeis4.)