%I M0852 N0324 #74 Oct 27 2023 09:59:50
%S 1,1,2,3,7,21,135,2470,175428,52980624
%N Number of NP-equivalence classes of self-dual threshold functions of n or fewer variables ; number of majority (i.e., decisive and weighted) games with n players.
%D 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.)
%D D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.1, p. 79.
%D S. Muroga, Threshold Logic and Its Applications. Wiley, NY, 1971, p. 38, Table 2.3.2. - Row 23. (Cases until n=9.)
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D J. von Neumann and O. Morgenstern, Theory of games and economic behavior, Princeton University Press, New Jersey, 1944. (Cases n=1 to 5.)
%H J.-C. Hausmann, <a href="http://arxiv.org/abs/1501.07553">Counting polygon spaces, Boolean functions and majority games</a>, arXiv preprint arXiv:1501.07553 [math.CO], 2015.
%H J.-C. Hausmann and E. Rodriguez, <a href="https://projecteuclid.org/euclid.em/1086894088">The space of clouds in Euclidean space</a>, Experiment. Math. 13 (2004), 31-47.
%H J.-C. Hausmann and E. Rodriguez. <a href="http://www.unige.ch/math/folks/hausmann/polygones">The space of clouds in Euclidean space</a>, Corrections and additional material.
%H J. R. Isbell, <a href="http://dx.doi.org/10.1090/S0025-5718-1959-0103129-5">On the enumeration of majority games</a>, MTAC, v.13, 1959, pp. 21-28. (Case n=7).
%H Alastair D. King, <a href="/A002080/a002080.pdf">Comments on A002080 and related sequences based on threshold functions</a>, Mar 17 2023.
%H 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 4, p. 213.
%H S. Muroga, <a href="/A000371/a000371.pdf">Threshold Logic and Its Applications</a>, Wiley, NY, 1971 [Annotated scans of a few pages]
%H S. Muroga, T. Tsuboi and C. R. Baugh, <a href="http://dx.doi.org/10.1109/T-C.1970.223046">Enumeration of threshold functions of eight variables</a>, IEEE Trans. Computers, 19 (1970), 818-825.
%H S. Muroga, T. Tsuboi and C. R. Baugh, <a href="/A002077/a002077.pdf">Enumeration of threshold functions of eight variables</a>, IEEE Trans. Computers, 19 (1970), 818-825. [Annotated scanned copy]
%H Erik Ordentlich, Ron M. Roth and Gadiel Seroussi, <a href="http://www.hpl.hp.com/techreports/2012/HPL-2012-113.pdf">On q-ary Antipodal Matchings and Applications</a>, 2012.
%H <a href="/index/Bo#Boolean">Index entries for sequences related to Boolean functions</a>
%F a(n) = Sum_{k=1..n} A003184(k). - Alastair D. King, Oct 26, 2023
%Y Cf. A000617, A002077-A002080, A003184, A109456, A132183, A189359.
%K nonn,nice,more
%O 1,3
%A _N. J. A. Sloane_
%E a(10) added by W. Lan (wl(AT)fjrtvu.edu.cn), Jun 27 2010
%E Better description from Alastair King, Mar 17, 2023.