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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
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
KEYWORD
nonn,more
AUTHOR
STATUS
approved

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