

A262068


Number of binary strings of length 2n that can be written as the concatenation of one or more squares.


1



1, 2, 6, 22, 76, 268, 926, 3250, 11328, 39658, 138534, 484364, 1693078, 5918780, 20690230, 72328158, 252841374, 883869956, 3089791576, 10801141656
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OFFSET

0,2


COMMENTS

By a "square" we mean a word of the form xx, where x is a string, like the English word "murmur".
a(0)=1 is by convention.  N. J. A. Sloane, Sep 17 2015


LINKS

Table of n, a(n) for n=0..19.


EXAMPLE

For n = 2 the six words are 0000, 0011, 0101, and their complements.


MAPLE

for n from 1 to 13 do
B[n]:= convert(map(t> tt, StringTools:Generate(n, "01")), set);
od:
C[0]:= {""}:
for n from 1 to 13 do
C[n]:= {seq(seq(seq(cat(s, t), s=B[i]), t = C[ni]), i=1..n)};
od:
seq(nops(C[n]), n=0..13); # Robert Israel, Sep 17 2015


CROSSREFS

Cf. A262278.
Sequence in context: A109194 A014334 A107239 * A148496 A217528 A181367
Adjacent sequences: A262065 A262066 A262067 * A262069 A262070 A262071


KEYWORD

nonn,more


AUTHOR

Jeffrey Shallit, Sep 17 2015


EXTENSIONS

a(14)a(19) from Lars Blomberg, Feb 03 2019


STATUS

approved



