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Period 12: repeat [1, 1, 0, 0, -1, -1, -1, -1, 0, 0, 1, 1].
0

%I #32 Jul 27 2022 08:29:03

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

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

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

%N Period 12: repeat [1, 1, 0, 0, -1, -1, -1, -1, 0, 0, 1, 1].

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,-1).

%F a(n) = H(floor((n + 4)/2), 1, 1/2) where H(n, a, b) = hypergeom([a - n/2, b - n/2], [1 - n], 4).

%F From _Chai Wah Wu_, Feb 16 2021: (Start)

%F a(n) = a(n-2) - a(n-4) for n > 3.

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

%o (Magma) &cat [[1, 1, 0, 0, -1, -1, -1, -1, 0, 0, 1, 1]^^10]

%K sign,easy

%O 0

%A _Peter Luschny_, Sep 03 2019