A000618 - OEIS

A000618

Number of nondegenerate Boolean functions of n variables: For n > 0, a(n) = A000616(n) - A000616(n-1).
(Formerly M0160 N0063)

2, 1, 3, 16, 380, 1227756, 400507805615570, 527471432057653003616766223882064, 11218076601767519586965281984173341005397671421797828020453197626398048

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

REFERENCES

S. Muroga, Threshold Logic and Its Applications. Wiley, NY, 1971, p. 38, Table 2.3.2. - Row 12.

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=0..8.

Aniruddha Biswas and Palash Sarkar, Counting Unate and Monotone Boolean Functions Under Restrictions of Balancedness and Non-Degeneracy, J. Int. Seq. (2025) Vol. 28, Art. No. 25.3.4. See p. 5.

Eiichi Goto and Hidetosi Takahasi, Some Theorems Useful in Threshold Logic for Enumerating Boolean Functions, in Proceedings International Federation for Information Processing (IFIP) Congress, 1962, pp. 747-752. [Annotated scans of certain pages]

Saburo Muroga, Threshold Logic and Its Applications, Wiley, NY, 1971 [Annotated scans of a few pages]

Saburo Muroga, T. Tsuboi and C. R. Baugh, Enumeration of threshold functions of eight variables, IEEE Trans. Computers, 19 (1970), 818-825. [Annotated scanned copy]

J. Sklansky, General synthesis of tributary switching networks, IEEE Trans. Elect. Computers, 12 (1963), 464-469.

Index entries for sequences related to Boolean functions

FORMULA

For n > 0, a(n) = A000616(n) - A000616(n-1). - Charles R Greathouse IV, Oct 03 2008

EXAMPLE

From Michael B. Porter, Nov 03 2025: (Start)

The a(2) = 3 classes of Boolean functions of 2 variables are:

{x OR y, ~x OR y, x OR ~y, ~x OR ~y},

{x XOR y, ~x XOR y}, and

{x AND y, ~x AND y, x AND ~y, ~x AND ~y}.

The degenerate functions x, ~x, y, ~y, 1, and 0 are excluded. (End)

CROSSREFS