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!)
A305029 Period 10 sequence [ 0, 2, 2, 2, 2, 0, -2, -2, -2, -2, ...] except a(0) = 1. 1

%I

%S 1,2,2,2,2,0,-2,-2,-2,-2,0,2,2,2,2,0,-2,-2,-2,-2,0,2,2,2,2,0,-2,-2,-2,

%T -2,0,2,2,2,2,0,-2,-2,-2,-2,0,2,2,2,2,0,-2,-2,-2,-2,0,2,2,2,2,0,-2,-2,

%U -2,-2,0,2,2,2,2,0,-2,-2,-2,-2,0,2,2,2,2,0,-2,-2,-2,-2

%N Period 10 sequence [ 0, 2, 2, 2, 2, 0, -2, -2, -2, -2, ...] except a(0) = 1.

%C If m is odd, (Sum_{k=0..m} x^k)/(Sum_{k=0..m} (-x)^k) = (1+x)/(1-x).

%H Seiichi Manyama, <a href="/A305029/b305029.txt">Table of n, a(n) for n = 0..10000</a>

%F G.f.: (1 + x + x^2 + x^3 + x^4)/(1 - x + x^2 - x^3 + x^4).

%F a(n) = C(2*n,n) mod 2 + 1/5*(-(n mod 10)+((n+4) mod 10)+((n+5) mod 10)-((n+9) mod 10)). - _Paolo P. Lava_, Jun 08 2018

%p 1,seq(1/5*(-(n mod 10)+((n+4) mod 10)+((n+5) mod 10)-((n+9) mod 10)),n=1..80); # _Paolo P. Lava_, Jun 08 2018

%o (PARI) N=66; x='x+O('x^N); Vec(((sum(k=0, 4, x^k))/(sum(k=0, 4, (-x)^k))))

%Y Cf. A040000 (m is odd), A000007 (m=0), A184334 (m=2), this sequence (m=4).

%K easy,sign

%O 0,2

%A _Seiichi Manyama_, May 24 2018

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 May 18 16:07 EDT 2021. Contains 343995 sequences. (Running on oeis4.)