%I #27 Apr 18 2022 10:14:30
%S 3,16,152,2326,52132,1602420,64529264
%N The index of Simon's piecewise testability congruence, for words of length 2 over an nletter alphabet.
%C Consider an alphabet with n letters, say {a_0, a_1, ... a_{n1} }. 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.
%C Define two words to be 2equivalent if they have the same subsequences of length up to 2. The nth term of this sequence is the number of equivalence classes of this equivalence relation, when the size of the alphabet is n.
%H Prateek Karandikar and Philippe Schnoebelen, <a href="http://arxiv.org/abs/1310.1278">On the index of Simon's congruence for piecewise testability</a> arXiv:1310.1278 [cs.FL], 20132014.
%e For n=1, with the alphabet {a_0}, representatives of the three equivalence classes are: empty word, a_0, a_0a_0.
%K nonn,more
%O 1,1
%A _Prateek Karandikar_ and _Philippe Schnoebelen_, Oct 09 2013
