%I #24 Mar 08 2024 01:12:36
%S 1,2,5,8,7,4,1,2,5,8,7,4,1,2,5,8,7,4,1,2,5,8,7,4,1,2,5,8,7,4,1,2,5,8,
%T 7,4,1,2,5,8,7,4,1,2,5,8,7,4,1,2,5,8,7,4,1,2,5,8,7,4,1,2,5,8,7,4,1,2,
%U 5,8,7,4,1,2,5,8,7,4,1,2,5,8,7,4,1,2
%N Period 6: repeat [1, 2, 5, 8, 7, 4].
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,-1,1).
%F From _R. J. Mathar_, Feb 25 2009, Mar 09 2009: (Start)
%F a(n) = a(n-1) - a(n-3) + a(n-4) for n>3.
%F G.f.: (1+x+3*x^2+4*x^3)/((1-x)*(1+x)*(x^2-x+1)). (End)
%F a(n) = (27-cos(n*Pi)-20*cos(n*Pi/3)-4*sqrt(3)*sin(n*Pi/3))/6. - _Wesley Ivan Hurt_, Jun 17 2016
%p A154127:=n->(27-cos(n*Pi)-20*cos(n*Pi/3)-4*sqrt(3)*sin(n*Pi/3))/6: seq(A154127(n), n=0..100); # _Wesley Ivan Hurt_, Jun 17 2016
%t Flatten[Table[{1, 2, 5, 8, 7, 4}, {20}]] (* _Wesley Ivan Hurt_, Jun 17 2016 *)
%o (PARI) a(n)=[1,2,5,8,7,4][n%6+1] \\ _Charles R Greathouse IV_, Jun 02 2011
%o (Magma) &cat[[1, 2, 5, 8, 7, 4]: n in [0..20]]; // _Wesley Ivan Hurt_, Jun 17 2016
%Y Cf. A020806, A029898, A070366, A141425, A146501, A153130.
%K nonn,easy,less
%O 0,2
%A _Paul Curtz_, Jan 05 2009
%E Corrected numerator in g.f _R. J. Mathar_, Mar 09 2009