A135017 a(n) is 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.

0, 0, 1, 0, 2, 1, 3, 5, 7, 15, 20, 48, 60, 156, 205, 489, 761, 1572, 2796, 5357, 10174, 19021, 37272, 69375, 137759, 258444, 513696, 976890, 1934900, 3727164, 7358675, 14316861, 28217028, 55288907, 108942267, 214462953, 422973649

Offset

1,5

Comments

These strings may be regarded as the "primitive" strings among those enumerated by A135473.

Equals the inverse binomial transform of A135473.

Links

Table of n, a(n) for n=1..37.

Index entries for doubling substrings

Formula

Empirically, grows like 2^n.

Example

n=3: abc
n=4: -
n=5: ababc, abcbc
n=6: abcabc
n=7: abababc, ababcbc, abcbcbc

Crossrefs

Cf. A135473.

Sequence in context: A076074 A319153 A286390 * A070168 A246646 A198094

Adjacent sequences: A135014 A135015 A135016 * A135018 A135019 A135020

Keyword

nonn

Author

David Applegate and N. J. A. Sloane, Feb 12 2008

Extensions

Extended to 37 terms by David Applegate, Feb 16 2008

Status

approved