0,3

N. Alon and V. H. Vu, Anti-Hadamard matrices, coin weighing, threshold gates and indecomposable hypergraphs, Journal of Combinatorial Theory A79 (1997), 133-160.

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).

For asymptotics see the Alon-Vu article.

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.

Sequence in context: A087312 A099170 A018095 this_sequence A006723 A096390 A092264

Adjacent sequences: A003214 A003215 A003216 this_sequence A003218 A003219 A003220

nonn,hard

N. J. A. Sloane (njas(AT)research.att.com).