A109456 Number of Boolean functions of n variables that are self-dual and regular.

0, 1, 1, 2, 3, 7, 21, 135, 2470, 319124, 1214554343, 1706241214185942

Offset

0,4

Comments

Or, number of self-dual 2-monotonic Boolean functions of n or fewer variables.

Agrees with A001532 for n <= 8 but then diverges.

The value for n=10 was calculated with BDD techniques; all solutions are characterized by a binary decision diagram with 30011986 nodes.

The value for n=11 was calculated by Minfeng Wang in May 2012 (see [Hausmann & Rodriguez). The news was published by J.-C. Hausmann (2015). - Fabián Riquelme, Mar 19 2018

For n from 1 to 9, a(n) agrees with the number of directed zero-sum games with n players in Table 1 of Krohn and Sudhölter. - Peter Bala, Dec 16 2021

References

D. E. Knuth, The Art of Computer Programming, Vol. 4, Section 7.1.1 (in preparation).

Links

Table of n, a(n) for n=0..11.

J.-C. Hausmann, Counting polygon spaces, Boolean functions and majority games, arXiv preprint arXiv:1501.07553 [math.CO], 2015.

Jean-Claude Hausmann & Eugenio Rodriguez, The space of clouds in an Euclidean space, Corrections and additional material, 2014.

I. Krohn and P. Sudhölter, Directed and weighted majority games, Mathematical Methods of Operation Research, 42, 2 (1995), 189-216. See Table 1, row 4, p. 213; also on ResearchGate.

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

Crossrefs

Sequence in context: A262305 A189360 A001532 * A155745 A067738 A296287

Adjacent sequences: A109453 A109454 A109455 * A109457 A109458 A109459

Keyword

nonn,hard,more

Author

Don Knuth, Aug 17 2005

Extensions

a(10) from Don Knuth, Feb 06 2008

a(11) from Fabián Riquelme, Mar 27 2018

Status

approved