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 A135017 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. 4

%I

%S 0,0,1,0,2,1,3,5,7,15,20,48,60,156,205,489,761,1572,2796,5357,10174,

%T 19021,37272,69375,137759,258444,513696,976890,1934900,3727164,

%U 7358675,14316861,28217028,55288907,108942267,214462953,422973649

%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.

%K nonn

%O 1,5

%A _David Applegate_ and _N. J. A. Sloane_, Feb 12 2008

%E Extended to 37 terms by David Applegate, Feb 16 2008

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