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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 (list; graph; refs; listen; history; text; internal format)
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), 159-164.

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

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Last modified February 23 21:23 EST 2018. Contains 299588 sequences. (Running on oeis4.)