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!)
A041982 Numerators of continued fraction convergents to sqrt(514). 2
22, 23, 68, 1519, 3106, 4625, 206606, 211231, 629068, 14050727, 28730522, 42781249, 1911105478, 1953886727, 5818878932, 129969223231, 265757325394, 395726548625, 17677725464894, 18073452013519 (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 (0,0,0,0,0,9250,0,0,0,0,0,-1).

FORMULA

G.f.: (22 +23*x +68*x^2 +1519*x^3 +3106*x^4 +4625*x^5 +3106*x^6 -1519*x^7 +68*x^8 -23*x^9 +22*x^10 -x^11)/(1 -9250*x^6 +x^12). - Vincenzo Librandi, Nov 13 2013

a(n) = 9250*a(n-6)-a(n-12). - Vincenzo Librandi, Nov 12 2013

MATHEMATICA

Numerator[Convergents[Sqrt[514], 30]] ( or *) CoefficientList[Series[(22 + 23 x + 68 x^2 + 1519 x^3 + 3106 x^4 + 4625 x^5 + 3106 x^6 - 1519 x^7 + 68 x^8 - 23 x^9 + 22 x^10 - x^11)/(1 - 9250 x^6 + x^12), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 13 2013 *)

PROG

(MAGMA) I:=[22, 23, 68, 1519, 3106, 4625, 206606, 211231, 629068, 14050727, 28730522, 42781249]; [n le 12 select I[n] else 9250*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Nov 12 2013

CROSSREFS

Cf. A041983.

Sequence in context: A041986 A041988 A041984 * A252912 A041992 A041990

Adjacent sequences:  A041979 A041980 A041981 * A041983 A041984 A041985

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 August 4 13:53 EDT 2021. Contains 346447 sequences. (Running on oeis4.)