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A121981
Number of finite maximal bifix codes of degree n on a two-letter alphabet.
0
1, 1, 3, 73, 5056783
OFFSET
1,3
COMMENTS
A bifix (sometimes biprefix) code is a set of nonempty words X such that no word of X is a proper prefix or a proper suffix of another. The degree of a finite maximal bifix code X is the maximal number of parses that a word can have with respect to X.
It is known that there are finitely many finite maximal bifix codes of each degree.
REFERENCES
J. Berstel and D. Perrin, Theory of Codes, Academic Press, 1985, Chapter III.
EXAMPLE
On the alphabet {a,b}, for n=3 the a(3)=3 codes are:
{aaa,aab,aba,abb,baa,bab,bba,bbb},
{aaa,aaba,aabb,ab,baa,baba,babb,bba,bbb},
{aaa,aab,abaa,abab,abb,ba,bbaa,bbab,bbb}
CROSSREFS
Sequence in context: A145675 A373784 A336873 * A337413 A337409 A215961
KEYWORD
nonn,hard
AUTHOR
Alessandro De Luca, Feb 09 2011
STATUS
approved