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Base-4 digits are, in order, the first n terms of the periodic sequence with initial period 1,3,0,2.
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%I #9 Oct 13 2015 16:17:54

%S 1,7,28,114,457,1831,7324,29298,117193,468775,1875100,7500402,

%T 30001609,120006439,480025756,1920103026,7680412105,30721648423,

%U 122886593692,491546374770,1966185499081,7864741996327,31458967985308

%N Base-4 digits are, in order, the first n terms of the periodic sequence with initial period 1,3,0,2.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,0,0,1,-4).

%F G.f.: ( x*(1+3*x+2*x^3) ) / ( (x-1)*(4*x-1)*(1+x)*(x^2+1) ). - _R. J. Mathar_, Oct 13 2015

%t Module[{nn=30,d},d=PadRight[{},nn,{1,3,0,2}];Table[FromDigits[ Take[ d,n],4],{n,nn}]] (* _Harvey P. Dale_, Feb 11 2015 *)

%K nonn,base

%O 1,2

%A _Clark Kimberling_