A001320 Number of self-complementary Boolean functions of n variables: see Comments for precise definition. (Formerly M2982 N1204)

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

Offset

1,2

Comments

Number of self-complementary equivalence classes under the group C_{2^n} of all 2^n complementations of variables. - R. J. Mathar, Apr 14 2010

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

References

M. A. Harrison, The number of equivalence classes of Boolean functions under groups containing negation, IEEE Trans. Electron. Comput. 12 (1963), 559-561.

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..9.

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

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

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 *)

Crossrefs

Cf. A000610.

Sequence in context: A288563 A081383 A351139 * A133028 A144985 A168590

Adjacent sequences: A001317 A001318 A001319 * A001321 A001322 A001323

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

More terms from Vladeta Jovovic, Feb 23 2000

Status

approved