

A229954


The index of Simon's piecewise testability congruence, for words of length 2 over a nletter alphabet.


0




OFFSET

1,1


COMMENTS

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.
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.


LINKS

Table of n, a(n) for n=1..7.
Prateek Karandikar and Philippe Schnoebelen, On the index of Simon's congruence for piecewise testability arXiv:1310.1278 [cs.FL], 20132014.


EXAMPLE

For n=1, with the alphabet {a_0}, representatives of the three equivalence classes are : empty word, a_0, a_0a_0.


CROSSREFS

Sequence in context: A217251 A125281 A086371 * A228513 A135753 A191959
Adjacent sequences: A229951 A229952 A229953 * A229955 A229956 A229957


KEYWORD

nonn,more


AUTHOR

Prateek Karandikar and Philippe Schnoebelen, Oct 09 2013


STATUS

approved



