A176563 - OEIS

%I #41 Dec 12 2023 07:40:18

%S 1,-3,1,1,1,-3,1,1,1,-3,1,1,1,-3,1,1,1,-3,1,1,1,-3,1,1,1,-3,1,1,1,-3,

%T 1,1,1,-3,1,1,1,-3,1,1,1,-3,1,1,1,-3,1,1,1,-3,1,1,1,-3,1,1,1,-3,1,1,1,

%U -3,1,1,1,-3,1,1,1,-3,1,1,1,-3,1,1,1,-3,1,1,1,-3,1,1,1,-3,1,1,1,-3,1,1,1

%N Period 4: repeat [1, -3, 1, 1].

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

%F Sum_{k>=0} a(k)/(k+1) = 0.

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

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

%F a(n) = -a(n-1) -a(n-2) -a(n-3) for n>2. [_R. J. Mathar_, Apr 28 2010]

%F a(n) = 1-(1-(-1)^n)*(1-I^(n+1)). - _Bruno Berselli_, Mar 16 2011

%F Dirichlet generating function: Zeta(s)*(1 - 1/2^(s - 1))^2. [_Mats Granvik_ and _Jaume Oliver Lafont_, Mar 12 2014]

%F a(n) = a(n-4) for n>3. - _Wesley Ivan Hurt_, Jul 07 2016

%F E.g.f.: exp(-x) - 2*sin(x). - _Ilya Gutkovskiy_, Jul 07 2016

%p seq(op([1, -3, 1, 1]), n=0..50); # _Wesley Ivan Hurt_, Jul 07 2016

%t PadRight[{}, 100, {1, -3, 1, 1}] (* _Wesley Ivan Hurt_, Jul 07 2016 *)

%o (PARI) a(n)=[1,-3,1,1][n%4+1]

%o (Magma) &cat [[1, -3, 1, 1]^^30]; // _Wesley Ivan Hurt_, Jul 07 2016

%K sign,easy

%O 0,2

%A _Jaume Oliver Lafont_, Apr 20 2010