[seqfan] Re: What is the difference between A000610 and A001320?

[Richard Mathar]

On behalf of http://list.seqfan.eu/pipermail/seqfan/2010-April/004331.html :

One might add a comment to A000610:

   Number of self-complementary classes of the group G_n (a permutation group
   on the domain of boolean functions, containing the symmetric group S_n
   and the group C_{2^n} of a ll 2^n complementations of variables).

and a comment to A001320:

   Number of self-complementary classes of the group C_{2^n}
   of all 2^n complementations of variables.

and a comment to A000133:

   Number of classes of functions on the group C_{2^n} on the domain
   {0,1}^n and with the negation group on {0,1}.

The indexing in the formula in A001320 is wrong and the sum should
be replaced by a closed form:


%F A001320 a(n) = 2^(2^(n-1)) * (2^n-1) / 2^n. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 24 2006, corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 14 2010
%F A001320 a(n) = A016031(n)*A000079(n-1). [R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 14 2010]


Richard J. Mathar