OFFSET
1,2
COMMENTS
These are distinct groups of Boolean functions of n variables that output an equal number of 0s and 1s across all possible inputs (balanced), and cannot be transformed into each other by negating or permuting inputs. - Aniruddha Biswas, Nov 12 2024
REFERENCES
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
Herman Jamke, Table of n, a(n) for n = 1..10
B. Elspas, Self-complementary symmetry types of Boolean functions, IEEE Trans. Electron. Computers, 9 (1960), 264-266.
B. Elspas, Self-complementary symmetry types of Boolean functions, IEEE Transactions on Electronic Computers 2, no. EC-9 (1960): 264-266. [Annotated scanned copy]
E. M. Palmer and R. W. Robinson, Enumeration of self-dual configurations, Pacific J. Math., 110 (1984), 203-221. [From Herman Jamke (hermanjamke(AT)fastmail.fm), Aug 21 2010]
D. Zeilberger, First 7 terms of the sequence of weight-enumerators enumerating equivalence classes of Boolean functions under permutation of variable and negation . [From Herman Jamke (hermanjamke(AT)fastmail.fm), Aug 21 2010]
FORMULA
a(n) ~ binomial(2^n, 2^(n-1)) / ( n! * 2^n ). - Aniruddha Biswas, Nov 12 2024
EXAMPLE
For n = 2 the a(2) = 2. Solutions are f(x,y)=x and f(x,y)=x⊕y; are two 2-variable NP-inequivalent balanced Boolean functions. - Aniruddha Biswas, Nov 12 2024
CROSSREFS
KEYWORD
nonn,nice,easy,changed
AUTHOR
EXTENSIONS
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Aug 21 2010, Sep 05 2010
STATUS
approved