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%I #21 Dec 12 2023 08:04:03
%S 1,2,4,-4,-2,-1,1,2,4,-4,-2,-1,1,2,4,-4,-2,-1,1,2,4,-4,-2,-1,1,2,4,-4,
%T -2,-1,1,2,4,-4,-2,-1,1,2,4,-4,-2,-1,1,2,4,-4,-2,-1,1,2,4,-4,-2,-1,1,
%U 2,4,-4,-2,-1,1,2,4,-4,-2,-1,1,2,4,-4,-2,-1,1,2
%N Period 6: repeat [1, 2, 4, -4, -2, -1].
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (-1,-1,-1,-1,-1).
%F a(n) == A141425(n) (mod 9). - _Paul Curtz_, Feb 08 2009
%F a(n) = ( (2*A141425(n)) mod 9) - A141425(n). - _Paul Curtz_, Feb 08 2009
%F G.f.: (1+x^4+3*x^3+7*x^2+3*x)/( (x+1)*(x^2-x+1)*(x^2+x+1) ). [Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009]
%F From _Wesley Ivan Hurt_, Jun 23 2016: (Start)
%F a(n) + a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5) = 0 for n>4.
%F a(n) = cos(n*Pi) + 2*sqrt(3)*cos(n*Pi/6)*sin(n*Pi/6) - sqrt(3)*cos(n*Pi/2)*sin(n*Pi/6) + 3*sin(n*Pi/6)*sin(n*Pi/2). (End)
%p A156283:=n->[1, 2, 4, -4, -2, -1][(n mod 6)+1]: seq(A156283(n), n=0..100); # _Wesley Ivan Hurt_, Jun 23 2016
%t PadRight[{}, 80, {1,2,4,-4,-2,-1}] (* or *) LinearRecurrence[{-1,-1,-1,-1,-1}, {1,2,4,-4,-2}, 80] (* _Harvey P. Dale_, May 29 2013 *)
%o (Magma) &cat [[1, 2, 4, -4, -2, -1]^^20]; // _Wesley Ivan Hurt_, Jun 23 2016
%Y Cf. A141425.
%K sign,easy
%O 0,2
%A _Paul Curtz_, Feb 07 2009
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