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 A229954 The index of Simon's piecewise testability congruence, for words of length 2 over an n-letter alphabet. 0
 3, 16, 152, 2326, 52132, 1602420, 64529264 (list; graph; refs; listen; history; text; internal format)
 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 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], 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 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

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Last modified June 14 20:28 EDT 2024. Contains 373401 sequences. (Running on oeis4.)