A002079 Number of N-equivalence classes of threshold functions of exactly n variables.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• more

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

• 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

Crossrefs

Cf. A002077, A002078, A002080.

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.

Extensions

Better description from Alastair King, Mar 17 2023.