A002077 Number of N-equivalence classes of self-dual threshold functions of exactly n variables. (Formerly M3683 N1503)

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

Offset

1,4

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

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

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.

Crossrefs

Cf. A002078, A002079, A002080.

Sequence in context: A331978 A210855 A324228 * A113096 A135078 A195243

Adjacent sequences: A002074 A002075 A002076 * A002078 A002079 A002080

Keyword

nonn,more

Author

N. J. A. Sloane

Extensions

Better description from Alastair King, Mar 17, 2023.

Status

approved