

A090702


a(n) is the minimal number k such that every binary word of length n can be transformed into a palindrome or an antipalindrome by deleting at most k letters.


1



0, 0, 1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 5, 5, 5, 6, 7, 7, 7, 8
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OFFSET

1,6


COMMENTS

A word l_0...l_n is called a palindrome if l_i=l_{ni} for all i<=n.
A binary word l_0...l_n is called an antipalindrome if l_i<>l_{ni} for all i<=n


REFERENCES

I. Protasov, Palindromial equivalence: one theorem and two problems, Matem. Studii, 14, #1, (2000), p. 111.
O. V. Ravsky, A New Measure of Asymmetry of Binary Words, Journal of Automata, Languages and Combinatorics, 8, #1 (2003), p. 7583.


LINKS

Table of n, a(n) for n=1..20.


FORMULA

a(n)>=[(n+2*[(n3)/7])/3] for every n and for 2<=n<=20 equality holds.


CROSSREFS

Cf. A090701.
Sequence in context: A055748 A284520 A342248 * A029124 A113512 A338624
Adjacent sequences: A090699 A090700 A090701 * A090703 A090704 A090705


KEYWORD

nonn,base


AUTHOR

Sasha Ravsky (oravsky(AT)mail.ru), Jan 12 2004


STATUS

approved



