%I #25 Mar 29 2021 15:07:09
%S 1,0,0,1,0,0,1,0,1,2,1,0,1,0,0,1,0,1,2,1,0,1,0,1,2,1,2,3,2,1,2,1,0,1,
%T 0,1,2,1,0,1,0,0,1,0,1,2,1,0,1,0,1,2,1,2,3,2,1,2,1,0,1,0,1,2,1,0,1,0,
%U 1,2,1,2,3,2,1,2,1,2,3,2,3,4,3,2,3,2,1,2,1,2,3,2,1,2,1,0,1,0,1,2,1,0,1,0,1
%N Number of zeros in balanced ternary representation of n.
%D D. E. Knuth, The Art of Computer Programming, Addison-Wesley, Reading, MA, Vol 2, pp 173-175.
%H Reinhard Zumkeller, <a href="/A134023/b134023.txt">Table of n, a(n) for n = 0..10000</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Balanced_ternary">Balanced Ternary</a>
%F a(n) = A134021(n) - A134022(n) - A134024(n).
%F a(n) = A134021(n) - A005812(n).
%e 100=1*3^4+1*3^3-1*3^2+0*3^1+1*3^0=='++-0+': a(100)=1;
%e 200=1*3^5-1*3^4+1*3^3+1*3^2+1*3^1-1*3^0=='+-+++-': a(200)=0;
%e 300=1*3^5+1*3^4-1*3^3+0*3^2+1*3^1+0*3^0=='++-0+0': a(300)=2.
%t Array[Count[If[First@ # == 0, Rest@ #, #], 0] &[Prepend[IntegerDigits[#, 3], 0] //. {a___, b_, 2, c___} :> {a, b + 1, -1, c}] &, 105, 0] (* _Michael De Vlieger_, Jun 27 2020 *)
%o (Python)
%o def a(n):
%o if n==0: return 1
%o s=0
%o x=0
%o while n>0:
%o x=n%3
%o n=n//3
%o if x==2:
%o x=-1
%o n+=1
%o if x==0: s+=1
%o return s
%o print([a(n) for n in range(101)]) # _Indranil Ghosh_, Jun 07 2017
%Y Cf. A005812, A059095, A134021, A134022, A134024.
%K nonn,base
%O 0,10
%A _Reinhard Zumkeller_, Oct 19 2007
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