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%I #49 Mar 08 2024 01:12:32
%S 1,5,7,2,4,8,1,5,7,2,4,8,1,5,7,2,4,8,1,5,7,2,4,8,1,5,7,2,4,8,1,5,7,2,
%T 4,8,1,5,7,2,4,8,1,5,7,2,4,8,1,5,7,2,4,8,1,5,7,2,4,8,1,5,7,2,4,8,1,5,
%U 7,2,4,8,1,5,7,2,4,8,1,5,7,2,4,8,1,5,7,2,4,8
%N Period 6: repeat [1, 5, 7, 2, 4, 8].
%C Also A141425^5 mod 9. See A020806.
%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_, Mar 08 2011: (Start)
%F a(n) = - a(n-1) + a(n-3) + a(n-4) for n>3.
%F G.f.: (2*x+1)^3 / ( (1-x)*(1+x)*(1+x+x^2) ). (End)
%F a(n) = (9-cos(n*Pi)-4*sqrt(3)*cos((1-4*n)*Pi/6))/2. - _Wesley Ivan Hurt_, Jun 17 2016
%p A153110:=n->(9-cos(n*Pi)-4*sqrt(3)*cos((1-4*n)*Pi/6))/2: seq(A153110(n), n=0..100); # _Wesley Ivan Hurt_, Jun 17 2016
%t PadLeft[{},90,{1,5,7,2,4,8}] (* _Harvey P. Dale_, Sep 10 2011 *)
%o (PARI) a(n)=[1,2,4,5,7,8][n%6+1] \\ _Charles R Greathouse IV_, Jun 02 2011
%o (Magma) &cat[[1, 5, 7, 2, 4, 8]: n in [0..20]]; // _Wesley Ivan Hurt_, Jun 17 2016
%Y Cf. A020806, A038194, A141425.
%K nonn,easy
%O 0,2
%A _Paul Curtz_, Dec 18 2008
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