A137748 Number of different strings of length n obtained from "abcdefgh" by iteratively duplicating any substring.

0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 43, 196, 814, 3188, 12018, 44178, 159660, 570262, 2019964, 7112774, 24940259, 87191430, 304203350

Offset

0,10

Comments

See A137743 for more comments.

Links

Table of n, a(n) for n=0..22.

Index entries for doubling substrings

Example

a(k) = 0 for k<8, since no shorter string can be obtained by duplication of substrings.
a(8) = 1 = # { abcdefgh }.
a(9) = 8 = # { aabcdefgh, abbcdefgh, abccdefgh, abcddefgh, abcdeefgh, abcdeffgh, abcdefggh, abcdefghh }.
a(10) = (8+1)*(8+2)/2-2 = 43:
for each letter we have one string of the form aaabcdefgh;
for each 2-element subset {a,b}, {a,c}, ... we have the string with each of these two letters duplicated (i.e., aabbcdefgh, aabccdefgh, ...),
and for each of ab,bc,cd,...,gh we have the string with this substring duplicated (ababcdefgh,...,abcdefghgh).

Prog

(PARI) A135473(14, 8) /* function defined in A137743 */

Crossrefs

Cf. A137740-A137743, A135473, A137744-A137747.

Sequence in context: A036647 A000429 A055853 * A005024 A094865 A122880

Adjacent sequences: A137745 A137746 A137747 * A137749 A137750 A137751

Keyword

more,nonn

Author

M. F. Hasler, Feb 10 2008

Extensions

a(15)-a(17) from Alois P. Heinz, Sep 01 2011

a(18)-a(20) from Lars Blomberg, Jan 12 2013

a(21)-a(22) from Bert Dobbelaere, Dec 30 2018

Status

approved