%I #14 Sep 08 2022 08:46:06
%S 0,1,-1,0,0,-1,1,0,1,-1,0,0,-1,1,0,1,-1,0,0,-1,1,0,1,-1,0,0,-1,1,0,1,
%T -1,0,0,-1,1,0,1,-1,0,0,-1,1,0,1,-1,0,0,-1,1,0,1,-1,0,0,-1,1,0,1,-1,0,
%U 0,-1,1,0,1,-1,0,0,-1,1,0,1,-1,0,0,-1,1,0,1,-1,0,0,-1,1,0,1,-1,0,0,-1,1
%N Period 7: repeat [0, 1, -1, 0, 0, -1, 1].
%C This is the sequence called c(n) in A234044 used in a formula for 2*exp(2*Pi*n*I/7) together with five other sequences: a(n) = A234044(n), b(n) = A234045(n), A(n) = A238468(n), B(n) = A238469(n) and C(n) = A238470(n). An example for n=4 is also given there.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (-1,-1,-1,-1,-1,-1).
%F G.f.: x*(1 - x - x^4 + x^5)/(1 - x^7).
%F a(n+7) = a(n), n>=0, with a(0) = a(3) = a(4) = 0 and a(1) = -a(2) = -a(5) = a(6) = 1.
%F From _Wesley Ivan Hurt_, Jul 19 2016: (Start)
%F a(n) + a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5) + a(n-6) = 0 for n>5.
%F a(n) = - floor(n/7) + 2*floor((1+n)/7) - floor((2+n)/7) + floor((4+n)/7) - 2*floor((5+n)/7) + floor((6+n)/7). (End)
%p seq(op([0, 1, -1, 0, 0, -1, 1]), n=0..20); # _Wesley Ivan Hurt_, Jul 19 2016
%t PadRight[{}, 100, {0, 1, -1, 0, 0, -1, 1}] (* _Wesley Ivan Hurt_, Jul 19 2016 *)
%o (Magma) &cat [[0, 1, -1, 0, 0, -1, 1]^^20]; // _Wesley Ivan Hurt_, Jul 19 2016
%Y Cf. A234044, A234045, A238468, A238469, A238470.
%K sign,easy
%O 0
%A _Wolfdieter Lang_, Feb 27 2014