A002080 Number of N-equivalence classes of self-dual threshold functions of n or fewer variables.

1, 2, 4, 12, 81, 1684, 122921, 33207256, 34448225389

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• more

References

• S. Muroga, Threshold Logic and Its Applications. Wiley, NY, 1971, p. 38 and 214.
• 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.
• 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. A000609, A002077, A002078.

Formula

a(n) = Sum_{k=1..n} A002077(k)*binomial(n,k) = (1/2^n)*Sum_{k=1..n} A000609(k-1)*binomial(n,k). - Alastair D. King, Mar 17 2023.

Extensions

Better description and corrected value of a(7) from Alastair King (see link) - N. J. A. Sloane, Oct 24 2023