%I #23 Feb 16 2025 08:33:11
%S 2,12,232,63056,4221224224,18295693635288736320,
%T 338921575014037816709507133224870496384,
%U 115563265193225535967792084153637585725267224878335215248443107599191173632256
%N Lexicographically largest binary de Bruijn sequences, B(2,n).
%C Term a(n) is a cyclical bit string of length 2^n, with every possible substring of length n occurring exactly once.
%C Mathworld says: "Every de Bruijn sequence corresponds to an Eulerian cycle on a de Bruijn graph. Surprisingly, it turns out that the lexicographic sequence of Lyndon words of lengths divisible by n gives the lexicographically earliest de Bruijn sequence (Ruskey). de Bruijn sequences can be generated by feedback shift registers (Golomb 1967; Ronse 1984; Skiena 1990, p. 196)."
%C Terms grow like Theta(2^(2^n)). - _Darse Billings_, Oct 18 2009
%H Darse Billings, <a href="/A166316/b166316.txt">Table of n, a(n) for n=1..9</a>
%H Darse Billings, <a href="/A166315/a166315.py.txt">Python program</a>
%H F. Ruskey, <a href="http://combos.org/necklace">Necklaces, Lyndon words, De Bruijn sequences, etc.</a>
%H F. Ruskey, <a href="/A000011/a000011.pdf">Necklaces, Lyndon words, De Bruijn sequences, etc.</a> [Cached copy, with permission, pdf format only]
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/deBruijnSequence.html">de Bruijn Sequence</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/De_Bruijn_sequence">de Bruijn Sequence</a>
%e For n = 3, the last de Bruijn sequence, a(n) = B(2,3), is '11101000' = 232.
%Y Cf. A166315 (lexicographically earliest de Bruijn sequences (binary complements)).
%K base,nonn,changed
%O 1,1
%A _Darse Billings_, Oct 11 2009
%E a(6)-a(8) from _Darse Billings_, Oct 18 2009