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EXAMPLE
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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).
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