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

Offset

0,8

Comments

See A137743 for more comments.

Links

Table of n, a(n) for n=0..23.

Index entries for doubling substrings

Example

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 }.

Prog

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

Crossrefs

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

Sequence in context: A186314 A234267 A055420 * A344504 A261064 A094811

Adjacent sequences: A137743 A137744 A137745 * A137747 A137748 A137749

Keyword

more,nonn

Author

M. F. Hasler, Feb 10 2008

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

Status

approved