A137745 Number of different strings of length n obtained from "abcde" by iteratively duplicating any substring.

0, 0, 0, 0, 0, 1, 5, 19, 66, 218, 700, 2218, 6997, 22064, 69662, 220395, 699090, 2224114, 7098773, 22733498, 73048903, 235504760, 761689193, 2471105355

Offset

0,7

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<5, since no shorter string can be obtained by duplicating a substring.
a(5) = # { abcde },
a(6) = # { aabcde, abbcde, abccde, abcdde, abcdee },
a(7) = # { aaabcde, aabbcde, aabccde, aabcdde, aabcdee, ababcde, abbbcde, abbccde, abbcdde, abbcdee, abcbcde, abcccde, abccdde, abccdee, abcdcde, abcddde, abcddee, abcdede, abcdeee }

Prog

(PARI) A135473(13, 5) /* function defined in A137743...*/

Crossrefs

Cf. A137740-A137743, A135473, A137744-A137748.

Sequence in context: A239618 A124806 A059509 * A005021 A067325 A273599

Adjacent sequences: A137742 A137743 A137744 * A137746 A137747 A137748

Keyword

more,nonn

Author

M. F. Hasler, Feb 10 2008

Extensions

a(14)-a(19) from Lars Blomberg, Jan 12 2013

a(20)-a(21) from Michael S. Branicky, Jan 05 2021

a(22)-a(23) from Bert Dobbelaere, Jun 10 2024

Status

approved