

A230127


Number of binary strings of length n avoiding "squares" (that is, repeated blocks of the form xx) with x > 1.


5



1, 2, 4, 8, 12, 20, 26, 38, 42, 52, 56, 56, 48, 42, 32, 22, 10, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET

0,2


COMMENTS

Entringer et al. showed that a(n) = 0 for all n >= 19.


LINKS

Table of n, a(n) for n=0..81.
Nathaniel Johnston, C code for computing this sequence
R. C. Entringer, D. E. Jackson and J. A. Schatz, On nonrepetitive sequences, J. Combin. Theory Ser. A. 16 (1974), 159164.


EXAMPLE

a(4) = 12 because there are 16 binary strings of length 4, but 4 of these strings (namely 0000, 0101, 1010, and 1111) repeat a substring of length 2. Thus a(4) = 16  4 = 12.
a(18) = 2 because there are 2 strings of length 18 not containing any "squares" of length greater than 1: 010011000111001101 and 101100111000110010.


CROSSREFS

Cf. A022087, A229614, A230177.
Sequence in context: A127405 A136034 A243112 * A059793 A118029 A049322
Adjacent sequences: A230124 A230125 A230126 * A230128 A230129 A230130


KEYWORD

nonn,fini,full


AUTHOR

Nathaniel Johnston, Oct 10 2013


STATUS

approved



