cp's OEIS Frontend

A132183 Number of "regular" Boolean functions of n variables.

%I A132183 #31 Dec 19 2021 17:10:00
%S A132183 2,3,5,10,27,119,1173,44315,16175190,284432730176
%N A132183 Number of "regular" Boolean functions of n variables.
%C A132183 The sequence also counts order ideals (or antichains) of the binary majorization lattice with 2^n points. That lattice for n=5 will be illustrated in Fig. 8 of Volume 4 of The Art of Computer Programming. The basic properties of this lattice will be discussed in exercise 7.1.1-109 of that book. (The material of Section 7.1.1 will be available in paperback in a couple months.)
%C A132183 Michael Somos (Mar 13 2012) asks if A003187 and A132187 are the same. - _N. J. A. Sloane_, Mar 13 2012
%C A132183 For n from 1 to 8, a(n) agrees with the number of directed games on n players in Table 1 of Krohn and Sudhölter. - _Peter Bala_, Dec 16 2021
%H A132183 Stefan Bolus, <a href="https://macau.uni-kiel.de/receive/diss_mods_00009114">A QOBDD-based Approach to Simple Games</a>, Dissertation, Doktor der Ingenieurwissenschaften der Technischen Fakultaet der Christian-Albrechts-Universitaet zu Kiel, 2012. - From _N. J. A. Sloane_, Dec 22 2012
%H A132183 Bjørn Kjos-Hanssen, Lei Liu, <a href="https://arxiv.org/abs/1902.00815">The number of languages with maximum state complexity</a>, arXiv:1902.00815 [cs.FL], 2019.
%H A132183 I. Krohn and P. Sudhölter, <a href="https://doi.org/10.1007/BF01415753">Directed and weighted majority games</a>, Mathematical Methods of Operation Research, 42, 2 (1995), 189-216. See Table 1, row 1, p. 213; also on <a href="https://www.researchgate.net/publication/226788682_Directed_and_weighted_majority_games">ResearchGate</a>.
%e A132183 For example, the 10 Boolean functions for n=3 have the truth tables
%e A132183   00000000
%e A132183   00000001
%e A132183   00000011
%e A132183   00000111
%e A132183   00001111
%e A132183   00010111
%e A132183   00011111
%e A132183   00111111
%e A132183   01111111
%e A132183   11111111
%e A132183 (things don't get very interesting until n=4 or 5).
%Y A132183 Cf. A003187.
%K A132183 nonn,more
%O A132183 0,1
%A A132183 _Don Knuth_, Nov 19 2007