A137747 Number of different strings of length n obtained from "abcdefg" by iteratively duplicating any substring.

0, 0, 0, 0, 0, 0, 0, 1, 7, 34, 143, 555, 2050, 7343, 25809, 89642, 308986, 1059786, 3623524, 12365973, 42160774, 143701920, 489891138, 1670965268

Offset

0,9

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<7, since no shorter string can be obtained by duplication of substrings.
a(7) = 1 = #{abcdefg},
a(8) = 7 = #{aabcdefg, abbcdefg, abccdefg, abcddefg, abcdeefg, abcdeffg, abcdefgg},
a(9) = 8*(8+1)/2-2 = 34:
for each letter we have one string of the form aaabcdefg;
for each 2-element subset {a,b}, {a,c}, ... we have the string with each of these two letters duplicated (i.e., aabbcdefg, aabccdefg, ...);
and for each of ab,bc,cd,...,fg we have the string with this substring duplicated (ababcdefg,...,abcdefgfg).
(See A137746 for the pattern.)

Prog

(PARI) A135473(14, 7) /* function defined in A137743 */

Crossrefs

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

Sequence in context: A326245 A219756 A014915 * A273722 A005023 A094256

Adjacent sequences: A137744 A137745 A137746 * A137748 A137749 A137750

Keyword

more,nonn

Author

M. F. Hasler, Feb 10 2008

Extensions

a(15)-a(20) from Lars Blomberg, Jan 12 2013

a(21) from Michael S. Branicky, Jan 07 2021

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

Status

approved