A003184 Number of NP-equivalence classes of self-dual threshold functions of exactly n variables. (Formerly M3492)

1, 0, 1, 1, 4, 14, 114, 2335, 172958, 52805196

Offset

1,5

References

H. M. Gurk and J. R. Isbell. 1959. Simple Solutions. In A. W. Tucker and R. D. Luce (eds.) Contributions to the Theory of Games, Volume 4. Princeton, NJ: Princeton University Press, pp. 247-265. Case n=6.

S. Muroga, Threshold Logic and Its Applications. Wiley, NY, 1971, p. 38, Table 2.3.2. - Row 24. (Cases n>7.)

J. von Neumann and O. Morgenstern, Theory of games and economic behavior, Princeton University Press, New Jersey, 1944. Cases n=1 to 5.

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=1..10.

J. R. Isbell, On the enumeration of majority games, MTAC, v. 13, 1959, pp. 21-28. (Case n=7.)

Alastair D. King, Comments on A002080 and related sequences based on threshold functions, Mar 17 2023.

S. Muroga, Threshold Logic and Its Applications, Wiley, NY, 1971 [Annotated scans of a few pages]

S. Muroga, T. Tsuboi and C. R. Baugh, Enumeration of threshold functions of eight variables, IEEE Trans. Computers, 19 (1970), 818-825. [Annotated scanned copy]

Index entries for sequences related to Boolean functions

Formula

a(n) = A001532(n) - A001532(n-1), for n > 1. - Evgeny Luttsev, Sep 09 2014

Crossrefs

Cf. A000619, A001532, A002077-A002080.

Sequence in context: A048369 A269590 A113559 * A065062 A240273 A137048

Adjacent sequences: A003181 A003182 A003183 * A003185 A003186 A003187

Keyword

nonn,more

Author

N. J. A. Sloane

Extensions

a(9) from Evgeny Luttsev, Sep 09 2014

Better description and new offset from Alastair King, Mar 17, 2023

Status

approved