cp's OEIS Frontend

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.

%I A001320 M2982 N1204 #34 Apr 18 2025 08:44:05
%S A001320 1,3,14,240,63488,4227858432,18302628885633695744,
%T A001320 338953138925153547590470800371487866880,
%U A001320 115565932813024562229384322928592814283244066726840484812818018414147674308608
%N 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.
%C A001320 The next term (a(10)) has 155 digits. - _Harvey P. Dale_, Jul 27 2011
%D A001320 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001320 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001320 M. A. Harrison, <a href="https://doi.org/10.1109/PGEC.1963.263656">The number of equivalence classes of Boolean functions under groups containing negation</a>, IEEE Trans. Electron. Comput. 12 (1963), 559-561.
%H A001320 M. A. Harrison, <a href="/A000370/a000370.pdf">The number of equivalence classes of Boolean functions under groups containing negation</a>, IEEE Trans. Electron. Comput. 12 (1963), 559-561. [Annotated scanned copy]
%H A001320 <a href="/index/Bo#Boolean">Index entries for sequences related to Boolean functions</a>
%F A001320 a(n) = 2^(2^(n-1)) * (2^n-1) / 2^n. - _Zerinvary Lajos_, Oct 24 2006, corrected by _R. J. Mathar_, Apr 14 2010
%F A001320 a(n) = A016031(n)*A000079(n-1). - _R. J. Mathar_, Apr 14 2010
%p A001320 a:=n->sum(((fermat(n)-1))/2^(j+1),j=0..n): seq(a(n), n=0..8); # _Zerinvary Lajos_, Oct 24 2006
%t A001320 Table[2^(2^(n-1))(2^n-1)/2^n,{n,10}] (* _Harvey P. Dale_, Jul 27 2011 *)
%Y A001320 Cf. A000610.
%K A001320 nonn,easy,nice
%O A001320 1,2
%A A001320 _N. J. A. Sloane_
%E A001320 More terms from _Vladeta Jovovic_, Feb 23 2000
%E A001320 Clarification to the definition by _R. J. Mathar_, Apr 14 2010, edited and incorporated into the name by _Andrey Zabolotskiy_, Apr 18 2025