A002079 Number of N-equivalence classes of threshold functions of exactly n variables. (Formerly M0122 N0049)

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

Offset

0,1

References

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

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

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=0..8.

Alastair D. King, Comments on A002080 and related sequences based on threshold functions, Mar 17 2023.

Muroga, Saburo, Iwao Toda, and Satoru Takasu, Theory of majority decision elements, Journal of the Franklin Institute 271.5 (1961): 376-418. [Annotated scans of pages 413 and 414 only]

S. Muroga, T. Tsuboi and C. R. Baugh, Enumeration of threshold functions of eight variables, IEEE Trans. Computers, 19 (1970), 818-825. [Annotated scanned copy]

Index entries for sequences related to Boolean functions

Formula

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.

Crossrefs

Cf. A002077, A002078, A002080.

Sequence in context: A173159 A271574 A274198 * A006126 A078357 A225432

Adjacent sequences: A002076 A002077 A002078 * A002080 A002081 A002082

Keyword

nonn,more

Author

N. J. A. Sloane

Extensions

Better description from Alastair King, Mar 17, 2023.

Status

approved