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COMMENT
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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
Number of Ouroborean rings for binary n-tuplets. - Lekraj Beedassy (blekraj(AT)yahoo.com), May 06 2004
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
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REFERENCES
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F. Harary and E. Palmer, Graphical Enumeration, (1973), p. 31.
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.
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Cor. 5.6.15.
I. Stewart, Game, Set and Math, pp. 50, Penguin 1991.
J. L. Gross and J. Yellen, eds., Handbook of Graph Theory, CRC Press, 2004; p. 255.
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