A107765 Number of nonisomorphic self-dual monotone Boolean functions of n variables (where the result depends on all n variables).

1, 0, 1, 1, 4, 23, 686

Offset: 1

Author

Don Knuth, Jun 11 2005

Keywords

• hard
• nonn
• more

Examples

			The four cases for n=5 can be represented as simple majority functions as follows:
maj(a,b,c,d,e); maj(a,a,b,b,c,d,e); maj(a,a,a,b,b,c,c,d,e); maj(a,a,a,b,c,d,e).
(Only 14 of the 23 cases for n=6 have a simple representation of this form.)
		

References

• S. Muroga. Threshold Logic and its Applications. Wiley, 1971.
• John von Neumann and Oskar Morgenstern, Theory of Games and Economic Behavior (1944), Section 52.5.

Crossrefs

Cf. A107766, A001206.

Cf. A008840 (larger class of Boolean functions = partial sums of A107765). - Olivier Gérard, Oct 11 2012

Extensions

a(7) from Vladeta Jovovic, Jun 13 2005