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!)
A042110 Numerators of continued fraction convergents to sqrt(580). 2
24, 289, 13896, 167041, 8031864, 96549409, 4642403496, 55805391361, 2683301188824, 32255419657249, 1550943444736776, 18643576756498561, 896442627756667704, 10775955109836511009, 518142287899909196136 (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 (0,578,0,-1).

FORMULA

G.f.: (24 + 289*x + 24*x^2 - x^3)/(1 - 578*x^2 + x^4). - Vincenzo Librandi, Nov 16 2013

a(n) = 578*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 16 2013

MATHEMATICA

Numerator[Convergents[Sqrt[580], 30]] (* or *) CoefficientList[Series[(24 + 289 x + 24 x^2 - x^3)/(1 - 578 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 16 2013 *)

LinearRecurrence[{0, 578, 0, -1}, {24, 289, 13896, 167041}, 20] (* Harvey P. Dale, Jun 21 2021 *)

PROG

(MAGMA) I:=[24, 289, 13896, 167041]; [n le 4 select I[n] else 578*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 16 2013

CROSSREFS

Cf. A042111.

Sequence in context: A035707 A035475 A288458 * A282993 A295272 A086941

Adjacent sequences:  A042107 A042108 A042109 * A042111 A042112 A042113

KEYWORD

nonn,cofr,frac,easy,less

AUTHOR

N. J. A. Sloane.

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 October 22 18:45 EDT 2021. Contains 348175 sequences. (Running on oeis4.)