A090701 a(n) is the minimal number k such that every binary word of length n can be divided into k palindromes.

1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 14, 14, 14, 14, 15, 15, 16, 16, 16, 16, 17, 17, 18, 18, 18, 18, 19, 19, 20, 20, 20, 20, 21, 21, 22, 22, 22, 22, 23, 23, 24, 24, 24, 24, 25, 25, 26, 26, 26, 26, 27, 27, 28, 28, 28, 28, 29, 29, 30, 30

Offset

1,2

Comments

A word l_0...l_n is called a palindrome if l_i=l_{n-i} for all i<=n.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..16384

A. Baababov, A "Pentium" is good but a mind is better, Kvant 4-5 (1999), 38-42. (in Russian)

O. V. Ravsky, On the palindromic decomposition of binary words, arXiv:1004.1278 [math.CO], 2010; Journal of Automata, Languages and Combinatorics, 8, #1 (2003), p. 71-74.

Formula

a(n) = floor(n/6) + floor((n+4)/6) + 1 for n<>11 and a(11)=5.

Mathematica

Array[Boole[# == 11] + Floor[#/6] + Floor[(# + 4)/6] + 1 &, 87] (* Michael De Vlieger, Jan 23 2018 *)

Prog

(PARI) a(n)=if(n==11, 5, floor(n/6)+floor((n+4)/6)+1); \\ Joerg Arndt, Jan 21 2018

Crossrefs

Cf. A090702.

Sequence in context: A194324 A194328 A194304 * A339332 A330996 A056970

Adjacent sequences: A090698 A090699 A090700 * A090702 A090703 A090704

Keyword

easy,nonn

Author

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

Extensions

More terms from Joerg Arndt, Jan 21 2018

Status

approved