A002079 - OEIS

%I M0122 N0049 #29 Oct 27 2023 03:36:28

%S 2,1,2,9,96,2690,226360,64646855,68339572672

%N Number of N-equivalence classes of threshold functions of exactly n variables.

%D S. Muroga, Threshold Logic and Its Applications. Wiley, NY, 1971, p. 38, Table 2.3.2. - Row 8.

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

%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).

%H Alastair D. King, <a href="/A002080/a002080.pdf">Comments on A002080 and related sequences based on threshold functions</a>, Mar 17 2023.

%H Muroga, Saburo, 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 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 <a href="/index/Bo#Boolean">Index entries for sequences related to Boolean functions</a>

%F A002078(n) = Sum_{k=0..n} a(k)*binomial(n,k). A000609(n) = Sum_{k=0..n} a(k)*binomial(n,k)*2^k. - Alastair D. King, Mar 17, 2023.

%Y Cf. A002077, A002078, A002080.

%K nonn,more

%O 0,1

%A _N. J. A. Sloane_

%E Better description from Alastair King, Mar 17, 2023.