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%I #14 Jul 02 2015 04:03:03
%S 1,2,3,6,11,21,42,83,166,331,661,1322,2643,5285,10569,21138,42275,
%T 84550,169099,338197,676394,1352787,2705573,5411146,10822291,21644582,
%U 43289163,86578325,173156650,346313299,692626597,1385253193,2770506386,5541012771,11082025542
%N The number of 0's in the n-th stage of A164349.
%C A164349 is generated as follows. Start with the string 01, and at each stage copy the previous string twice and remove the last symbol.
%C Since the number of symbols in the whole string is 2^n + 1, A164362 + A164363 = 2^n + 1.
%H Paul Tek, <a href="/A164362/b164362.txt">Table of n, a(n) for n = 1..3323</a>
%H Paul Tek, <a href="/A164362/a164362.pl.txt">PERL program for this sequence</a>
%F A recurrence is given in terms of A164364(n) = A164349(2^n).
%F a(n+1) = 2*a(n) + A164364(n) - 1.
%e 01 -> 010 -> 01001 -> 010010100 -> 01001010001001010 etc.
%e So the number of 0's in the n-th stage is the sequence 1, 2, 3, 6, 11 etc.
%t t = Nest[ Most@ Flatten@ {#, #} &, {0, 1}, 25]; Table[ Count[ Take[t, 2^n + 1], 0], {n, 0, 25}] (* _Robert G. Wilson v_, Aug 17 2009 *)
%Y Cf. A164349, A164363, A164364.
%K nonn
%O 1,2
%A _Jack W Grahl_, Aug 14 2009
%E a(23)-a(26) from _Robert G. Wilson v_, Aug 17 2009
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