A296657 Triangle whose n-th row is the concatenated sequence of all binary Lyndon words of length n in lexicographic order.

0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1

Offset

1

Links

Table of n, a(n) for n=1..105.

Formula

Row n is a concatenation of A001037(n) Lyndon words with total length A027375(n).

Example

Triangle of binary Lyndon words begins:
0,1,
01,
001,011,
0001,0011,0111,
00001,00011,00101,00111,01011,01111,
000001,000011,000101,000111,001011,001101,001111,010111,011111.

Mathematica

LyndonQ[q_]:=Array[OrderedQ[{q, RotateRight[q, #]}]&, Length[q]-1, 1, And]&&Array[RotateRight[q, #]&, Length[q], 1, UnsameQ];
Table[Select[Tuples[{0, 1}, n], LyndonQ], {n, 5}]

Crossrefs

Cf. A000002, A000045, A000358, A001037, A006206, A027375, A059966, A066099, A102659, A228369, A281013, A294859.

Sequence in context: A154104 A187976 A197879 * A082848 A078588 A175992

Adjacent sequences: A296654 A296655 A296656 * A296658 A296659 A296660

Keyword

nonn,tabf

Author

Gus Wiseman, Dec 18 2017

Status

approved