A003184 Number of NP-equivalence classes of self-dual threshold functions of exactly n variables.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• more

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

• 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

Crossrefs

Cf. A000619, A001532, A002077-A002080.

Formula

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

Extensions

a(9) from Evgeny Luttsev, Sep 09 2014

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