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A003217 Maximum of minimum total weight for threshold functions of n Boolean variables.
(Formerly M2455)
0
0, 1, 3, 5, 9, 17, 35, 79, 209 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

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).

LINKS

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

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: A099170 A251705 A018095 * A178717 A006723 A217097

Adjacent sequences:  A003214 A003215 A003216 * A003218 A003219 A003220

KEYWORD

nonn,hard

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified September 25 12:56 EDT 2017. Contains 292469 sequences.