A003217 Maximum of minimum total weight for threshold functions of n Boolean variables. (Formerly M2455)

0, 1, 3, 5, 9, 17, 35, 79, 209

Offset

0,3

References

S. Muroga, Threshold Logic and Its Applications. Wiley, NY, 1971, p. 268.

S. Muroga, T. Tsuboi and C. R. Baugh, "Enumeration of threshold functions of eight variables," IEEE Transactions on Computers, 19 (1970), 818-825.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=0..8.

Noga Alon and Van H. Vu, Anti-Hadamard Matrices, Coin Weighing, Threshold Gates, and Indecomposable Hypergraphs, Journal of Combinatorial Theory, Series A, Volume 79, Issue 1, July 1997, Pages 133-160.

Formula

For asymptotics see the Alon-Vu article.

Example

a(4)=9 because the threshold functions "majority of wwxxyz000" and "majority of wwwxxyz00" and "majority of wwwxxyyz0" cannot be described as majority of seven or five things, but no threshold function of w,x,y,z requires a majority of more than nine.

Crossrefs

Sequence in context: A251705 A351938 A018095 * A297011 A337780 A178717

Adjacent sequences: A003214 A003215 A003216 * A003218 A003219 A003220

Keyword

nonn,hard,more

Author

N. J. A. Sloane

Status

approved