A002080 Number of N-equivalence classes of self-dual threshold functions of n or fewer variables. (Formerly M1266 N0485)

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

Offset

1,2

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

Table of n, a(n) for n=1..9.

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

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.

Crossrefs

Cf. A000609, A002077, A002078.

Sequence in context: A114903 A038054 A003180 * A001206 A144295 A119489

Adjacent sequences: A002077 A002078 A002079 * A002081 A002082 A002083

Keyword

nonn,more

Author

N. J. A. Sloane

Extensions

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

Status

approved