login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A000370 Number of NPN-equivalence classes of Boolean functions of n or fewer variables.
(Formerly M1287 N0494)
9
1, 2, 4, 14, 222, 616126, 200253952527184, 263735716028826576482466871188128, 5609038300883759793482640992086670939164957990135057216103303119630336 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Number of Boolean functions distinct under complementation/permutation.
REFERENCES
M. A. Harrison, Introduction to Switching and Automata Theory. McGraw Hill, NY, 1965, p. 153.
D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.1, p. 79.
S. Muroga, Threshold Logic and Its Applications. Wiley, NY, 1971, p. 38, Table 2.3.2. - Row 16.
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
M. A. Harrison, The number of equivalence classes of Boolean functions under groups containing negation, IEEE Trans. Electron. Comput. 12 (1963), 559-561.
M. A. Harrison, The number of equivalence classes of Boolean functions under groups containing negation, IEEE Trans. Electron. Comput. 12 (1963), 559-561. [Annotated scanned copy]
M. A. Harrison, On asymptotic estimates in switching and automata theory, J. ACM, v. 13, no. 1, Jan. 1966, pp. 151-157.
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]
Juling Zhang, Guowu Yang, William N. N. Hung, Tian Liu, Xiaoyu Song, Marek A. Perkowski, A Group Algebraic Approach to NPN Classification of Boolean Functions, Theory of Computing Systems (2018), 1-20.
FORMULA
a(n) is asymptotic to 2^{2^n} / ( n! * 2^{n+1} ) as n -> oo. This follows from a theorem of Michael Harrison. See Theorem 3 in Harrison (JACM, 1966). - Eric Bach, Aug 07 2017
CROSSREFS
Sequence in context: A368017 A061291 A166105 * A326941 A132531 A123052
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
More terms from Vladeta Jovovic, Feb 23 2000
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 28 04:16 EST 2024. Contains 370379 sequences. (Running on oeis4.)