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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A041962 Numerators of continued fraction convergents to sqrt(504). 2
22, 45, 202, 449, 19958, 40365, 181418, 403201, 17922262, 36247725, 162913162, 362074049, 16094171318, 32550416685, 146295838058, 325142092801, 14452547921302, 29230237935405, 131373499662922 (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 (0,0,0,898,0,0,0,-1).

FORMULA

G.f.: -(x^7-22*x^6+45*x^5-202*x^4-449*x^3-202*x^2-45*x-22)/(x^8-898*x^4+1). - Vincenzo Librandi, Nov 12 2013

a(n) = 898*a(n-4)-a(n-8). - Vincenzo Librandi, Nov 12 2013

MATHEMATICA

Numerator[Convergents[Sqrt[504], 30]] (* or *) CoefficientList[Series[-(x^7 - 22 x^6 + 45 x^5 - 202 x^4 - 449 x^3 - 202 x^2 - 45 x - 22)/(x^8 - 898 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 12 2013 *)

PROG

(MAGMA) I:=[22, 45, 202, 449, 19958, 40365, 181418, 403201]; [n le 8 select I[n] else 898*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 12 2013

CROSSREFS

Cf. A041963.

Sequence in context: A165309 A041960 A041958 * A041964 A041966 A106838

Adjacent sequences:  A041959 A041960 A041961 * A041963 A041964 A041965

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 December 2 22:46 EST 2021. Contains 349445 sequences. (Running on oeis4.)