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%I #19 Feb 06 2021 17:02:10
%S 0,0,0,1,0,0,0,1,0,0,0,1,1,1,1,2,0,0,0,1,0,0,0,1,0,0,0,1,1,1,1,2,0,0,
%T 0,1,0,0,0,1,0,0,0,1,1,1,1,2,1,1,1,2,1,1,1,2,1,1,1,2,2,2,2,3,0,0,0,1,
%U 0,0,0,1,0,0,0,1,1,1,1,2,0,0,0,1,0,0,0,1,0,0,0,1,1,1,1,2,0,0,0,1,0,0,0,1,0
%N Number of 3's in base-4 representation of n.
%H F. T. Adams-Watters and F. Ruskey, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL12/Ruskey2/ruskey14.html">Generating Functions for the Digital Sum and Other Digit Counting Sequences</a>, JIS 12 (2009) 09.5.6.
%F Recurrence relation: a(0) = 0, a(4m+3) = 1+a(m), a(4m) = a(4m+1) = a(4m+2) = a(m).
%F G.f.: (1/(1-z))*Sum_{m>=0} (z^(3*4^m)*(1 - z^(4^m))/(1 - z^(4^(m+1)))).
%F Morphism: 0, j -> j,j,j,j+1; e.g., 0 -> 0001 -> 0001000100011112 -> ...
%o (PARI) a(n) = #select(x->(x==3), digits(n, 4)); \\ _Michel Marcus_, Mar 24 2020
%Y Cf. A007090 (base 4), A160380 (0's), A160381 (1's), A160382 (2's).
%Y Cf. A283316 (mod 2).
%K nonn,base,easy
%O 0,16
%A _Frank Ruskey_, Jun 05 2009
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