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A194850 Number of prefix normal words of length n. 3
2, 3, 5, 8, 14, 23, 41, 70, 125, 218, 395, 697, 1273, 2279, 4185, 7568, 13997, 25500, 47414, 87024, 162456, 299947, 562345, 1043212, 1962589, 3657530, 6900717, 12910042, 24427486, 45850670, 86970163, 163756708, 311283363, 587739559, 1119581278, 2119042830 (list; graph; refs; listen; history; text; internal format)



A binary word of length n is prefix normal if for all 1 <= k <= n, no factor of length k has more a's than the prefix of length k. That is, abbabab is not prefix normal because aba has more a's than abb. - Zsuzsanna Liptak, Oct 12 2011

a(n) <= A062692(n): every prefix normal word is a pre-necklace, but the converse is not true, see the Fici/Lipták reference. - Joerg Arndt, Jul 20 2013


Peter Burcsi, G Fici, Z Lipták, F Ruskey, J Sawada, On prefix normal words and prefix normal forms, Preprint, 2016; http://www.cis.uoguelph.ca/~sawada/papers/pnf.pdf


Zsuzsanna Liptak, Table of n, a(n) for n = 1..50

P. Burcsi, G. Fici, Zs. Lipták, F. Ruskey, and J. Sawada, On Combinatorial Generation of Prefix Normal Words, arXiv:1401.6346 [cs.DS]

P. Burcsi, G. Fici, Z. Lipták, F. Ruskey, J. Sawada, Normal, Abby Normal, Prefix Normal, arXiv preprint arXiv:1404.2824, 2014

Péter Burcsi, Gabriele Fici, Zsuzsanna Lipták, Frank Ruskey, Joe, On Prefix Normal Words and Prefix Normal Forms, arXiv:1611.09017 [cs.DM], (2016)

G. Fici and Zs. Lipták, On Prefix Normal Words

G. Fici and Zs. Lipták, On Prefix Normal Words, Developments in Language Theory 2011, Lecture Notes in Computer Science 6795, 228-238.


For n=3: aaa, aab, abb, aba, bbb are all prefix normal words. - Zsuzsanna Liptak, Oct 12 2011


Cf. A062692 (binary pre-necklaces).

See A238109 for a list of the prefix-normal words.

Sequence in context: A005627 A191794 A191388 * A062692 A182024 A086661

Adjacent sequences:  A194847 A194848 A194849 * A194851 A194852 A194853




Gabriele Fici, Sep 04 2011


More terms added by Zsuzsanna Liptak, Oct 12 2011

Further terms added by Zsuzsanna Liptak, Jan 29 2014



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Last modified November 19 16:10 EST 2017. Contains 294936 sequences.