OFFSET
1,1
COMMENTS
Consider an alphabet with n letters, say {a_0, a_1, ... a_{n-1} }. For two words v and w over this alphabet, we say v embeds in w, or v is a subsequence of w, if v can be obtained from w by erasing some (occurrences of) letters.
Define two words to be 2-equivalent if they have the same subsequences of length up to 2. The n-th term of this sequence is the number of equivalence classes of this equivalence relation, when the size of the alphabet is n.
LINKS
Prateek Karandikar and Philippe Schnoebelen, On the index of Simon's congruence for piecewise testability arXiv:1310.1278 [cs.FL], 2013-2014.
EXAMPLE
For n=1, with the alphabet {a_0}, representatives of the three equivalence classes are: empty word, a_0, a_0a_0.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Prateek Karandikar and Philippe Schnoebelen, Oct 09 2013
STATUS
approved