login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A152892 Period 5: repeat [0, 3, 1, 0, 1]. 2

%I #24 Dec 12 2023 08:06:50

%S 0,3,1,0,1,0,3,1,0,1,0,3,1,0,1,0,3,1,0,1,0,3,1,0,1,0,3,1,0,1,0,3,1,0,

%T 1,0,3,1,0,1,0,3,1,0,1,0,3,1,0,1,0,3,1,0,1,0,3,1,0,1,0,3,1,0,1,0,3,1,

%U 0,1,0,3,1,0,1,0,3,1,0,1,0,3,1,0,1,0,3,1,0,1,0,3,1,0,1,0,3,1,0,1,0,3,1,0,1

%N Period 5: repeat [0, 3, 1, 0, 1].

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,1).

%F a(n+5) = a(n) with a(0) = a(3) = 0, a(1) = 3 and a(2) = a(4) = 1.

%F O.g.f: ((3*z+z^2+z^4)/(1-z^5)).

%F a(n) = 1 + (-1/2 + (3/10)*sqrt(5))*cos(2*n*Pi/5) + ((1/5)*sqrt(2)*sqrt(5 + sqrt(5)) + (1/10)*sqrt(2)*sqrt(5 - sqrt(5)))*sin(2*n*Pi/5) + (-1/2 - (3/10)*sqrt(5))*cos(4*n*Pi/5) + (-(1/10)*sqrt(2)*sqrt(5 + sqrt(5)) + (1/5)*sqrt(2)*sqrt(5-sqrt(5)))*sin(4*n*Pi/5).

%F a(n) = (n^3 + 2*n^2) mod 5. - _Gary Detlefs_, Mar 20 2010

%p seq((n^3+2*n^2)mod 5,n=0..50); # _Gary Detlefs_, Mar 20 2010

%t PadRight[{},120,{0,3,1,0,1}] (* _Harvey P. Dale_, Oct 04 2016 *)

%Y Cf. A026053, A026068.

%K easy,nonn

%O 0,2

%A _Richard Choulet_, Dec 14 2008

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)