A102560 - OEIS

%I #27 Dec 14 2023 05:17:59

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

%T -1,1,0,0,-1,1,0,0,-1,1,0,0,-1,1,0,0,-1,1,0,0,-1,1,0,0,-1,1,0,0,-1,1,

%U 0,0,-1,1,0,0,-1,1,0,0,-1,1,0,0,-1,1,0,0,-1,1,0,0,-1,1,0,0,-1,1,0,0,-1,1,0,0,-1,1,0,0,-1,1,0,0,-1,1,0,0,-1,1

%N Expansion of (1-x^3)/(1-x^4).

%C Period 4: repeat [1, 0, 0, -1].

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-1,-1,-1).

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

%F a(n) = (-1)^floor(n/2)/2+(-1)^n/2.

%F a(n) = cos(Pi*n/2)/2 + sin(Pi*n/2)/2 + cos(Pi*n)/2.

%F a(n) = -a(n-1)-a(n-2)-a(n-3) for n>2 with a(0)=1, a(1)=a(2)=0. - _Jaume Oliver Lafont_, Dec 05 2008

%p seq(op([1, 0, 0, -1]), n=0..50); # _Wesley Ivan Hurt_, Jul 06 2016

%t CoefficientList[ Series[(1 - x^3)/(1 - x^4), {x, 0, 105}], x] (* _Robert G. Wilson v_, Jan 15 2005 *)

%o (Magma) &cat [[1, 0, 0, -1]^^30]; // _Wesley Ivan Hurt_, Jul 06 2016

%o (PARI) x='x+O('x^50); Vec((1 - x^3)/(1 - x^4)) \\ _G. C. Greubel_, Jun 02 2017

%K easy,sign

%O 0,1

%A _Paul Barry_, Jan 14 2005