%N a(n) = number of strings of length n that can be obtained by starting with abc and repeatedly doubling any substring in place and then discarding any string that contains two successive equal letters.
%C These strings may be regarded as the "primitive" strings among those enumerated by A135473.
%C Equals the inverse binomial transform of A135473.
%H <a href="/index/Do#repeat">Index entries for doubling substrings</a>
%F Empirically, grows like 2^n.
%e n=3: abc
%e n=4: -
%e n=5: ababc, abcbc
%e n=6: abcabc
%e n=7: abababc, ababcbc, abcbcbc
%Y Cf. A135473.
%A _David Applegate_ and _N. J. A. Sloane_, Feb 12 2008
%E Extended to 37 terms by David Applegate, Feb 16 2008