

A229614


Number of binary strings of length n avoiding "squares" (that is, repeated blocks of the form xx) with x > 2.


3



1, 2, 4, 8, 16, 32, 56, 104, 178, 314, 536, 930, 1558, 2666, 4482, 7574, 12686, 21360, 35812, 60152, 100812, 169122, 283498, 475356, 796292, 1334558, 2235888, 3746534, 6276048, 10515080, 17614726, 29510362, 49434792, 82815016, 138729368, 232399846, 389306052
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OFFSET

0,2


COMMENTS

Entringer et al. showed that this sequence is always nonzero (in contrast with A230127, which is zero for all n >= 19).  Nathaniel Johnston, Oct 10 2013


LINKS

Table of n, a(n) for n=0..36.
R. C. Entringer, D. E. Jackson and J. A. Schatz, On nonrepetitive sequences, J. Combin. Theory Ser. A. 16 (1974), 159164.


EXAMPLE

For n = 6 there are 8 strings omitted, namely 000000, 001001, ..., 111111, so a(6) = 648 = 56.


CROSSREFS

Cf. A230127, A230177, A230216.
Sequence in context: A176718 A033860 A231388 * A230216 A245392 A115909
Adjacent sequences: A229611 A229612 A229613 * A229615 A229616 A229617


KEYWORD

nonn


AUTHOR

Jeffrey Shallit, Sep 26 2013


EXTENSIONS

a(23)a(36) from Nathaniel Johnston, Oct 10 2013


STATUS

approved



