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Base-3 digits are, in order, the first n terms of the periodic sequence with initial period 1,1,0.
1

%I #15 Dec 24 2015 13:39:32

%S 1,4,12,37,112,336,1009,3028,9084,27253,81760,245280,735841,2207524,

%T 6622572,19867717,59603152,178809456,536428369,1609285108,4827855324,

%U 14483565973,43450697920,130352093760,391056281281,1173168843844,3519506531532,10558519594597

%N Base-3 digits are, in order, the first n terms of the periodic sequence with initial period 1,1,0.

%H Colin Barker, <a href="/A033130/b033130.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,1,-3).

%F a(n) = 3*a(n-1) + a(n-3) - 3*a(n-4).

%F G.f.: x*(1+x) / ((1-x)*(1-3*x)*(1+x+x^2)). - _Colin Barker_, Dec 24 2015

%t Module[{nn=30,c},c=PadRight[{},nn,{1,1,0}];Table[FromDigits[Take[c,n],3],{n,nn}]] (* or *) LinearRecurrence[{3,0,1,-3},{1,4,12,37},30] (* _Harvey P. Dale_, Sep 01 2015 *)

%o (PARI) Vec(x*(1+x)/((1-x)*(1-3*x)*(1+x+x^2)) + O(x^30)) \\ _Colin Barker_, Dec 24 2015

%K nonn,base,easy

%O 1,2

%A _Clark Kimberling_