A000614 Number of complemented types of Boolean functions of n variables under action of AG(n,2). (Formerly M0815 N0307)

2, 3, 6, 18, 206, 7888299, 8112499583888855378066, 42287533217833953489054778023401252726576585396037133766

Offset

1,1

Comments

From Philippe Langevin's article: Let m be a positive integer. The space of Boolean functions from GF(2)^m into GF(2) is denoted by RM(k,m). This notation comes from coding theory, where it is the Reed-Muller code of order k in m variables. The affine group AG(2, m) acts on the spaces RM(k,m), and thus on RM(k,m)/RM(s,m) when s <= k. - Jonathan Vos Post, Feb 08 2011

References

R. J. Lechner, Harmonic Analysis of Switching Functions, in A. Mukhopadhyay, ed., Recent Developments in Switching Theory, Ac. Press, 1971, pp. 121-254, esp. p. 186.

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..8.

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 the classification of Boolean functions by the general linear and affine groups, J. Soc. Indust. Appl. Math. 12 (1964) 285-299.

Philippe Langevin, Classification of Boolean functions under the affine group, Oct 31, 2009.

Index entries for sequences related to Boolean functions

Crossrefs

Cf. A000214.

Sequence in context: A185625 A114302 A000304 * A233239 A018290 A364645

Adjacent sequences: A000611 A000612 A000613 * A000615 A000616 A000617

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

More terms and better description from Vladeta Jovovic, Feb 24 2000

Status

approved