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Period 6: repeat [3, 4, 0, 5, 6, 3].
2

%I #17 Dec 12 2023 08:09:14

%S 3,4,0,5,6,3,3,4,0,5,6,3,3,4,0,5,6,3,3,4,0,5,6,3,3,4,0,5,6,3,3,4,0,5,

%T 6,3,3,4,0,5,6,3,3,4,0,5,6,3,3,4,0,5,6,3,3,4,0,5,6,3,3,4,0,5,6,3,3,4,

%U 0,5,6,3,3,4,0,5,6,3,3,4,0,5,6,3,3,4,0,5,6,3,3,4,0,5,6,3,3,4,0,5,6,3,3,4,0

%N Period 6: repeat [3, 4, 0, 5, 6, 3].

%C Also the decimal expansion of 1135210/333333 or the continued fraction of (81+sqrt(9867))/58.

%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*(3+4*x+5*x^3+6*x^4+3*x^5) / ((1-x)*(1+x)*(1+x+x^2)*(x^2-x+1)).

%F a(n) = a(n-6) for n>6.

%F a(n) = cos(n*Pi/6)^2 * (39 - 36*cos(n*Pi/3) + 6*cos(2*n*Pi/3) - 4*sqrt(3)*sin(n*Pi/3))/3. - _Wesley Ivan Hurt_, Jun 23 2016

%p A158677:=n->[3, 4, 0, 5, 6, 3][(n mod 6)+1]: seq(A158677(n), n=0..100); # _Wesley Ivan Hurt_, Jun 23 2016

%t PadRight[{}, 120, {3,4,0,5,6,3}] (* _Harvey P. Dale_, Aug 06 2013 *)

%o (Magma) &cat [[3, 4, 0, 5, 6, 3]^^20]; // _Wesley Ivan Hurt_, Jun 23 2016

%Y Cf. A158674.

%K nonn,easy

%O 1,1

%A _Paul Curtz_, Mar 24 2009

%E Edited and extended by _R. J. Mathar_, Sep 07 2009