|
%I #19 Feb 26 2022 12:47:08
%S 0,0,0,0,0,0,0,0,1,8,43,196,814,3188,12018,44178,159660,570262,
%T 2019964,7112774,24940259,87191430,304203350
%N Number of different strings of length n obtained from "abcdefgh" by iteratively duplicating any substring.
%C See A137743 for more comments.
%H <a href="/index/Do#repeat">Index entries for doubling substrings</a>
%e a(k) = 0 for k<8, since no shorter string can be obtained by duplication of substrings.
%e a(8) = 1 = # { abcdefgh }.
%e a(9) = 8 = # { aabcdefgh, abbcdefgh, abccdefgh, abcddefgh, abcdeefgh, abcdeffgh, abcdefggh, abcdefghh }.
%e a(10) = (8+1)*(8+2)/2-2 = 43:
%e for each letter we have one string of the form aaabcdefgh;
%e for each 2-element subset {a,b}, {a,c}, ... we have the string with each of these two letters duplicated (i.e., aabbcdefgh, aabccdefgh, ...),
%e and for each of ab,bc,cd,...,gh we have the string with this substring duplicated (ababcdefgh,...,abcdefghgh).
%o (PARI) A135473(14,8) /* function defined in A137743 */
%Y Cf. A137740-A137743, A135473, A137744-A137747.
%K more,nonn
%O 0,10
%A _M. F. Hasler_, Feb 10 2008
%E a(15)-a(17) from _Alois P. Heinz_, Sep 01 2011
%E a(18)-a(20) from _Lars Blomberg_, Jan 12 2013
%E a(21)-a(22) from _Bert Dobbelaere_, Dec 30 2018
|
