A001320 Number of self-complementary Boolean functions of n variables, up to equivalence under the group (C_2)^n of all 2^n complementations of variables.

1, 3, 14, 240, 63488, 4227858432, 18302628885633695744, 338953138925153547590470800371487866880, 115565932813024562229384322928592814283244066726840484812818018414147674308608

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

Comments

The next term (a(10)) has 155 digits. - Harvey P. Dale, Jul 27 2011

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

• 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]
• Index entries for sequences related to Boolean functions

Crossrefs

Cf. A000610.

Programs

Maple

a:=n->sum(((fermat(n)-1))/2^(j+1),j=0..n): seq(a(n), n=0..8); # Zerinvary Lajos, Oct 24 2006

Mathematica

Table[2^(2^(n-1))(2^n-1)/2^n,{n,10}] (* Harvey P. Dale, Jul 27 2011 *)

Formula

a(n) = 2^(2^(n-1)) * (2^n-1) / 2^n. - Zerinvary Lajos, Oct 24 2006, corrected by R. J. Mathar, Apr 14 2010

a(n) = A016031(n)*A000079(n-1). - R. J. Mathar, Apr 14 2010

Extensions

More terms from Vladeta Jovovic, Feb 23 2000

Clarification to the definition by R. J. Mathar, Apr 14 2010, edited and incorporated into the name by Andrey Zabolotskiy, Apr 18 2025