

A000616


a(1)=1 by convention; for n >= 0, a(n) = number of irreducible Boolean functions of n variables.
(Formerly M0819 N0310 N1026)


22




OFFSET

1,2


COMMENTS

Number of NPequivalence classes of switching functions of n or fewer variables.
Number of inequivalent binary nonlinear codes of length n (and all sizes).
a(n+1) = number of NPNequivalence classes of canalizing functions (see A102449) with n variables. NPNequivalence allows complementing the function value as well as the individual variables. E.g., the 6 inequivalent canalizing functions when n=3 are 0, x, x AND y, x AND y AND z, x AND (y OR z), x AND (y XOR z).  Don Knuth, Aug 24 2005, Aug 06 2006


REFERENCES

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 112.
M. A. Harrison, The number of transitivity sets of Boolean functions, J. Soc. Indust. Appl. Math., 11 (1963), 806828.
M. A. Harrison, Introduction to Switching and Automata Theory. McGraw Hill, NY, 1965, p. 149.
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 11.
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).
I. Tomescu, Introducere in Combinatorica. Editura Tehnica, Bucharest, 1972, p. 129.


LINKS

Marcus Ritt, Table of n, a(n) for n = 1..10
B. Elspas, Selfcomplementary symmetry types of Boolean functions, IEEE Transactions on Electronic Computers 2, no. EC9 (1960): 264266. [Annotated scanned copy]
Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018.
R. K. Guy, Letter to N. J. A. Sloane, Mar 1974
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), 818825. [Annotated scanned copy]
J. Sklansky, General synthesis of tributary switching networks, IEEE Trans. Elect. Computers, 12 (1963), 464469.
I. Toda, On the number of types of selfdual logical functions, IEEE Trans. Electron. Comput., 11 (1962), 282284.
I. Toda, On the number of types of selfdual logical functions (annotated scanned copy)
Index entries for sequences related to Boolean functions


FORMULA

Harrison gives a simple formula in terms of the cycle index of the appropriate group.


CROSSREFS

Row sums of A039754.
Cf. A102449, A109460, A109462.
Sequence in context: A173249 A303584 A261014 * A233217 A261963 A183179
Adjacent sequences: A000613 A000614 A000615 * A000617 A000618 A000619


KEYWORD

nonn,easy,nice


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Vladeta Jovovic
Entry revised by N. J. A. Sloane, Aug 07 2006
Terms a(9) and a(10) (given in bfile) from Marcus Ritt, Aug 13 2013


STATUS

approved



