cp's OEIS Frontend

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

%I A003184 M3492 #57 Jun 28 2025 16:13:58
%S A003184 1,0,1,1,4,14,114,2335,172958,52805196
%N A003184 Number of NP-equivalence classes of self-dual threshold functions of exactly n variables.
%D A003184 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 A003184 S. Muroga, Threshold Logic and Its Applications. Wiley, NY, 1971, p. 38, Table 2.3.2. - Row 24. (Cases n>7.)
%D A003184 J. von Neumann and O. Morgenstern, Theory of games and economic behavior, Princeton University Press, New Jersey, 1944. Cases n=1 to 5.
%D A003184 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003184 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 A003184 Alastair D. King, <a href="/A002080/a002080.pdf">Comments on A002080 and related sequences based on threshold functions</a>, Mar 17 2023.
%H A003184 S. Muroga, <a href="/A000371/a000371.pdf">Threshold Logic and Its Applications</a>, Wiley, NY, 1971 [Annotated scans of a few pages]
%H A003184 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 A003184 <a href="/index/Bo#Boolean">Index entries for sequences related to Boolean functions</a>
%F A003184 a(n) = A001532(n) - A001532(n-1), for n > 1. - _Evgeny Luttsev_, Sep 09 2014
%Y A003184 Cf. A000619, A001532, A002077-A002080.
%K A003184 nonn,more
%O A003184 1,5
%A A003184 _N. J. A. Sloane_
%E A003184 a(9) from _Evgeny Luttsev_, Sep 09 2014
%E A003184 Better description and new offset from Alastair King, Mar 17 2023