A000610 Number of self-complementary Boolean functions of n variables: see Comments for precise definition.

0, 1, 2, 6, 42, 4094, 98210640, 148947659711650464, 872404773126414633407736134582136832, 88627167739308536281147085615274891669779458770791192509009429292662497280

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• easy

Comments

Number of self-complementary equivalence classes under the group G_n (a permutation group on the domain of Boolean functions, generated by the symmetric group S_n and the group (C_2)^n of all 2^n complementations of variables). - R. J. Mathar, Apr 14 2010

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

• B. Elspas, Self-complementary symmetry types of Boolean functions, IEEE Transactions on Electronic Computers 2, no. EC-9 (1960): 264-266. [Annotated scanned copy]
• 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]
• E. M. Palmer and R. W. Robinson, Enumeration of self-dual configurations Pacific J. Math., 110 (1984), 203-221.
• I. Toda, On the number of types of self-dual logical functions, IEEE Trans. Electron. Comput., 11 (1962), 282-284.
• I. Toda, On the number of types of self-dual logical functions (annotated scanned copy)
• Index entries for sequences related to Boolean functions

Crossrefs

Cf. A001320, A000370, A317794.

Programs

Python

# Using function get_num_equiv_bool_func from A000370.
[get_num_equiv_bool_func(n,True) for n in range(1,10)] # Gregory Morse, Dec 23 2024

Formula

a(n) = A000370(n) - A317794(n). - Tilman Piesk, Apr 14 2025

Extensions

More terms from Vladeta Jovovic, Feb 23 2000

a(0)=0 from Tilman Piesk, Apr 15 2025