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, 835145308, 1649638479, 3263689911, 6457465848, 12795025182, 25355766038, 50304700910

Offset: 1

Author

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

Keywords

• nonn

Comments

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

Equals the inverse binomial transform of A135473.

Examples

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

Links

• Index entries for doubling substrings

Crossrefs

Cf. A135473.

Formula

Empirically, grows like 2^n.

Extensions

Extended to 37 terms by David Applegate, Feb 16 2008

a(38)-a(44) by Martin Fuller, Jun 06 2025