Search: id:A016031
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%I A016031
%S A016031 1,1,2,16,2048,67108864,144115188075855872,
%T A016031 1329227995784915872903807060280344576,
%U A016031 226156424291633194186662080095093570025917938800079226639565593765455331328
%N A016031 De Bruijn's sequence: 2^(2^(n-1) - n): ways of arranging 2^n bits in 
               circle so all 2^n consecutive strings of length n are distinct.
%C A016031 Sequence corresponds also to the largest number that may be determined 
               by asking no more than 2^(n-1) - 1 questions("Yes"-or-"No" answerable)with 
               lying allowed at most once. - Lekraj Beedassy (blekraj(AT)yahoo.com), 
               Jul 15 2002
%C A016031 Number of Ouroborean rings for binary n-tuplets. - Lekraj Beedassy (blekraj(AT)yahoo.com), 
               May 06 2004
%C A016031 Also the number of games of Nim that are wins for the second player when 
               the starting position is either the empty heap or heaps of sizes 
               1 <= t_1 < t_2 < ... < t_k < 2^(n-1) (if n is 1, the only starting 
               position is the empty heap). E.g.: a(4) = 16: the winning positions 
               for the second player when all the heap sizes are different and less 
               than 2^3: (4,5,6,7), (3,5,6), (3,4,7), (2,5,7), (2,4,6), (2,3,6,7), 
               (2,3,4,5), (1,6,7), (1,4,5), (1,3,5,7), (1,3,4,6), (1,2,5,6), (1,
               2,4,7), (1,2,3), (1,2,3,4,5,6,7) and the empty heap. - Kennan Shelton 
               (kennan.shelton(AT)gmail.com), Apr 14 2006
%D A016031 F. Harary and E. Palmer, Graphical Enumeration, (1973), p. 31.
%D A016031 D. J. Newman, "A variation of the Game of Twenty Question", Prob. 66-20 
               pp. 121-2 In Problems in Applied Mathematics, Ed. M. S. Klamkin, 
               SIAM PA 1990.
%D A016031 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see 
               Cor. 5.6.15.
%D A016031 I. Stewart, Game, Set and Math, pp. 50, Penguin 1991.
%D A016031 J. L. Gross and J. Yellen, eds., Handbook of Graph Theory, CRC Press, 
               2004; p. 255.
%H A016031 R. Erra, N. Lygeros and N. Stewart, <a href="http://www.dmtcs.org/pdfpapers/
               dmAA0112.pdf">On Minimal Strings Containing the Elements of S(n) 
               by Decimation; Section 5.4</a>
%H A016031 Wikipedia, <a href="http://en.wikipedia.org/wiki/De_Bruijn_sequence">
               De Bruijn sequence</a>
%F A016031 a(n)=2^{A000295(n-1)}. - Lekraj Beedassy (blekraj(AT)yahoo.com), Jan 
               17 2007
%p A016031 P:=proc(n) local i,j; for i from 1 by 1 to n do j:=2^(2^(i-1)-i); print(j); 
               od; end: P(20); - Paolo P. Lava (ppl(AT)spl.at), May 11 2006
%Y A016031 Sequence in context: A102103 A060597 A091479 this_sequence A001309 A132569 
               A165644
%Y A016031 Adjacent sequences: A016028 A016029 A016030 this_sequence A016032 A016033 
               A016034
%K A016031 nonn,easy,nice
%O A016031 1,3
%A A016031 N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)

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