A137746 Number of different strings of length n obtained from "abcdef" by iteratively duplicating any substring.

0, 0, 0, 0, 0, 0, 1, 6, 26, 100, 360, 1246, 4217, 14102, 46861, 155212, 513336, 1697264, 5614670, 18594258, 61671770, 204907302, 682110940, 2275141754, 7603690251, 25462152854, 85428752530, 287163766530, 967046587261, 3262356284310, 11024401089607, 37315689561280, 126506891234231

Offset: 0

Author

M. F. Hasler, Feb 10 2008

Keywords

• nonn

Comments

See A137743 for more comments.

Examples

			a(k) = 0 for k<6, since no shorter string can be obtained by duplication
a(6) = 1 = # { abcdef },
a(7) = 6 = # { aabcdef, abbcdef, abccdef, abcddef, abcdeef, abcdeff },
a(8) = 26 = # { aaabcdef, aabbcdef, aabccdef, aabcddef, aabcdeef, aabcdeff, ababcdef, abbbcdef, abbccdef, abbcddef, abbcdeef, abbcdeff, abcbcdef, abcccdef, abccddef, abccdeef, abccdeff, abcdcdef, abcdddef, abcddeef, abcddeff, abcdedef, abcdeeef, abcdeeff, abcdefef, abcdefff }.
		

Links

• Index entries for doubling substrings

Crossrefs

Cf. A137740, A137741, A137742, A137743, A135473, A137744, A137745, A137746, A137747, A137748.

Programs

PARI

A135473(14,6) /* function defined in A137743 ... */

Extensions

a(15)-a(16) from Alois P. Heinz, Aug 31 2011

a(17)-a(19) from Lars Blomberg, Jan 12 2013

a(20)-a(21) from Michael S. Branicky, Jan 06 2021

a(22)-a(23) from Bert Dobbelaere, Jun 11 2024

a(24)-a(32) from Martin Fuller, Jun 07 2025