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%I #29 Mar 12 2024 12:17:20
%S 0,0,1,2,0,3,0,0,1,2,0,3,0,0,1,2,0,3,0,0,1,2,0,3,0,0,1,2,0,3,0,0,1,2,
%T 0,3,0,0,1,2,0,3,0,0,1,2,0,3,0,0,1,2,0,3,0,0,1,2,0,3,0,0,1,2,0,3,0,0,
%U 1,2,0,3,0,0,1,2,0,3,0,0,1,2
%N Period 6: repeat [0, 0, 1, 2, 0, 3].
%C Floretion Algebra Multiplication Program, FAMP Code: 1em[I]sumseq[ - .25'i - .5'j - .25i' - .5j' + .25'ii' + .25'jj' - .75'kk' + .25'jk' + .25'kj' + .25e]; sumtype: (Y[15], *, sum)
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,1).
%F G.f.: x^2*(1 + 2*x + 3*x^3)/((1 - x)*(x + 1)*(x^2 + x + 1)*(x^2 - x + 1)). [corrected by _Georg Fischer_, May 15 2019]
%F a(n) = (3 - cos(n*Pi/3) - 2*cos(n*Pi) - sqrt(3)*sin(n*Pi/3) - 2*sqrt(3)*sin(2*n*Pi/3)) / 3. - _Wesley Ivan Hurt_, Apr 26 2020
%t PadRight[{}, 100, {0, 0, 1, 2, 0, 3}] (* or *)
%t LinearRecurrence[{0, 0, 0, 0, 0, 1}, {0, 0, 1, 2, 0, 3}, 100] (* _Georg Fischer_, May 15 2019 *)
%o (PARI) a(n)=[0, 0, 1, 2, 0, 3][n%6+1]; \\ _Georg Fischer_, May 15 2019
%K nonn,easy
%O 0,4
%A _Creighton Dement_, Aug 22 2005
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