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%I #30 Feb 26 2024 02:01:05
%S 1,1,1,3,3,3,1,1,1,3,3,3,1,1,1,3,3,3,1,1,1,3,3,3,1,1,1,3,3,3,1,1,1,3,
%T 3,3,1,1,1,3,3,3,1,1,1,3,3,3,1,1,1,3,3,3,1,1,1,3,3,3,1,1,1,3,3,3,1,1,
%U 1,3,3,3,1,1,1,3,3,3,1,1,1,3,3,3,1,1,1,3,3,3,1,1,1,3,3,3,1,1,1,3,3,3,1,1,1
%N Period 6: repeat [1, 1, 1, 3, 3, 3].
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,-1,1).
%F G.f.: (1+3*x^3)/((1-x)*(1+x)*(1-x+x^2)). - _R. J. Mathar_, Nov 15 2007
%F a(n) = 2 - (2/3)*cos((1/3)*Pi*n) - (2/3)*3^(1/2)*sin((1/3)*Pi*n) + (1/3)*(-1)^(1+n). - _R. J. Mathar_, Nov 15 2007
%F a(n) = 2 - (-1)^floor(n/3). - _Bruno Berselli_, Jul 09 2013
%F a(n) = a(n-1) - a(n-3) + a(n-4) for n > 3. - _Wesley Ivan Hurt_, Jun 20 2016
%p A130974:=n->[1, 1, 1, 3, 3, 3][(n mod 6)+1]: seq(A130974(n), n=0..100); # _Wesley Ivan Hurt_, Jun 20 2016
%t PadRight[{}, 100, {1, 1, 1, 3, 3, 3}] (* _Wesley Ivan Hurt_, Jun 20 2016 *)
%o (Magma) &cat [[1, 1, 1, 3, 3, 3]^^30]; // _Wesley Ivan Hurt_, Jun 20 2016
%o (PARI) a(n) = [1, 1, 1, 3, 3, 3][n%6+1]; \\ _Jinyuan Wang_, Feb 26 2020
%Y Cf. A177957 (decimal expansion of (12+3*sqrt(35))/19). - _Klaus Brockhaus_, May 16 2010
%K nonn,easy
%O 0,4
%A _Paul Curtz_, Sep 28 2007
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