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A137748 Number of different strings of length n obtained from "abcdefgh" by iteratively duplicating any substring. 11
0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 43, 196, 814, 3188, 12018, 44178, 159660, 570262, 2019964, 7112774, 24940259, 87191430, 304203350 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,10
COMMENTS
See A137743 for more comments.
LINKS
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
Sequence in context: A036647 A000429 A055853 * A005024 A094865 A122880
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

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)