

A277133


Number of distinct sets of periods of length >= ceiling(n/2) in all binary strings of length n.


1



1, 2, 2, 4, 4, 7, 7, 11, 11, 17, 17, 25, 25, 35, 35, 48, 48, 65, 65, 86, 86, 113, 113, 143, 143, 180, 180, 227, 227, 284, 284, 346, 346, 421, 421, 508, 508, 610, 610, 726, 726, 861
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OFFSET

1,2


COMMENTS

A period of a string x of length n is an integer p such that x[i] = x[i+p] for 1 <= i <= np.
Alternatively, the number of distinct sets of border lengths, restricted to at most n/2 in length, possible over all binary strings of length n. A border of a word is a nonempty prefix that is also a suffix.
Alternatively, the number of distinct sets of lengths of palindromes that can begin a binary word of length n. (End)


LINKS



EXAMPLE

For n = 5, the possible sets of periods of length >=3 are {5}, {3,5}, {4,5}, {3,4,5}, achieved by the strings 00001, 01001, 00010, 00100, respectively.


CROSSREFS

Cf. A005434, which is the sequence where there is no restriction on the size of the periods.


KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



