A002077 Number of N-equivalence classes of self-dual threshold functions of exactly n variables.

1, 0, 1, 4, 46, 1322, 112519, 32267168, 34153652752

Offset: 1

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 10.
• S. Muroga and I. Toda, Lower bound on the number of threshold functions, IEEE Trans. Electron. Computers, 17 (1968), 805-806.
• 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.
• S. Muroga, Threshold Logic and Its Applications, Wiley, NY, 1971 [Annotated scans of a few pages]
• 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. A002078, A002079, A002080.

Formula

A002080(n) = Sum_{k=1..n} a(k)*binomial(n,k). Also A000609(n-1) = Sum_{k=1..n} a(k)*binomial(n,k)*2^k. - Alastair D. King, Mar 17 2023.

Extensions

Better description from Alastair King, Mar 17 2023