For $n \ge 2$, there is at least one binary DeBruijn sequence beginning with $n$ zeros followed by $n$ ones. Is there a straightforward way to construct such a sequence for each $n \ge 2$? Examples:


$n=2: 0011$


$n=3: 00011101$


$n=4: 0000111101100101$


$n=5: 00000111110111001101011000101001$



How to construct particular De Bruijn sequences
The answer is the construction of the De Bruijn sequence by concatenating certain Lyndon words as indicated [here](https://en.wikipedia.org/wiki/Lyndon_word) or, in this [article](http://emoreno.uai.cl/publicaciones/PREPRINTS/preprint-WORDS03-Lyndon_words_and_de_Bruijn_sequences_in_a_subshift_of_finite_type.pdf); that construction also guarantees the existence of the specific De Bruijn sequences you are looking for. 


A very comprehensible hands on explanation of the construction can found [here](http://royvanrijn.com/blog/2011/02/generating-de-bruijn-sequences-and-lyndon-words). 


