cp's OEIS Frontend

A000619 NP-equivalence classes of threshold functions of exactly n variables.

%I A000619 M0121 N0048 #49 Jun 27 2025 21:47:06
%S A000619 2,1,2,5,17,92,994,28262,2700791,990331318
%N A000619 NP-equivalence classes of threshold functions of exactly n variables.
%D A000619 S. Muroga, Threshold Logic and Its Applications. Wiley, NY, 1971, p. 38, Table 2.3.2. - Row 15.
%D A000619 S. Muroga, T. Tsuboi and C. R. Baugh, Enumeration of threshold functions of eight variables, IEEE Trans. Computers, 19 (1970), 818-825.
%D A000619 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000619 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000619 Eiichi Goto and Hidetosi Takahasi, <a href="/A000371/a000371_1.pdf">Some Theorems Useful in Threshold Logic for Enumerating Boolean Functions</a>, in Proceedings International Federation for Information Processing (IFIP) Congress, 1962, pp. 747-752. [Annotated scans of certain pages]
%H A000619 Vadim M. Kartak, Artem V. Ripatti, Guntram Scheithauer, and Sascha Kurz, <a href="https://doi.org/10.1016/j.dam.2015.02.020">Minimal proper non-IRUP instances of the one-dimensional cutting stock problem</a>, Discrete Applied Mathematics 2015, 187, 120-129. (has the last known term as of 2021, a(9)=990331318)
%H A000619 S. Muroga, <a href="/A000371/a000371.pdf">Threshold Logic and Its Applications</a>, Wiley, NY, 1971 [Annotated scans of a few pages]
%H A000619 Saburo Muroga, Iwao Toda, and Satoru Takasu, <a href="/A002079/a002079.pdf">Theory of majority decision elements</a>, Journal of the Franklin Institute 271.5 (1961): 376-418. [Annotated scans of pages 413 and 414 only]
%H A000619 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]
%F A000619 a(n) = A000617(n) - A000617(n-1). - Alastair D. King, Oct 26 2023.
%Y A000619 Cf. A000617.
%K A000619 nonn,more
%O A000619 0,1
%A A000619 _N. J. A. Sloane_
%E A000619 a(9) added by _Xavier Molinero_, Oct 06 2021