login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A042008 Numerators of continued fraction convergents to sqrt(527). 2

%I

%S 22,23,505,528,23737,24265,533302,557567,25066250,25623817,563166407,

%T 588790224,26469936263,27058726487,594703192490,621761918977,

%U 27952227627478,28573989546455,628006008103033

%N Numerators of continued fraction convergents to sqrt(527).

%H Vincenzo Librandi, <a href="/A042008/b042008.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 1056, 0, 0, 0, -1).

%F G.f.: -(x^7-22*x^6+23*x^5-505*x^4-528*x^3-505*x^2-23*x-22)/(x^8-1056*x^4+1). - _Vincenzo Librandi_, Nov 13 2013

%F a(n) = 1056*a(n-4)-a(n-8). - _Vincenzo Librandi_, Nov 13 2013

%t Numerator[Convergents[Sqrt[527], 30]] (* or *) CoefficientList[Series[-(x^7 - 22 x^6 + 23 x^5 - 505 x^4 - 528 x^3 - 505 x^2 - 23 x - 22)/(x^8 - 1056 x^4 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 13 2013 *)

%t LinearRecurrence[{0,0,0,1056,0,0,0,-1},{22,23,505,528,23737,24265,533302,557567},30] (* _Harvey P. Dale_, Sep 01 2017 *)

%o (MAGMA) I:=[22, 23, 505, 528, 23737, 24265, 533302, 557567]; [n le 8 select I[n] else 1056*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Nov 13 2013

%Y Cf. A042009.

%K nonn,cofr,frac,easy,less

%O 0,1

%A _N. J. A. Sloane_.

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 March 25 01:17 EDT 2019. Contains 321450 sequences. (Running on oeis4.)