A051502 Number of asymmetric types of Boolean functions of n variables under action of complementing group C(n,2).

2, 1, 2, 23, 3904, 134156284, 288230371925149328, 2658455991569831727504985413859223552, 452312848583266388373324160190187139712882738675004907244383829401569627136

Offset: 0

Author

Vladeta Jovovic

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..11
• Index entries for sequences related to Boolean functions

Programs

Mathematica

Table[1/(2^n)*Sum[(-1)^j*2^(Binomial[j, 2])*QBinomial[n, j, 2]*2^(2^(n-j)), {j,0,n}], {n,0,10}] (* G. C. Greubel, Feb 15 2018 *)

Formula

a(n) = (1/2^n)*Sum_{j=0..n} (-1)^j*2^(C(j, 2))*[ n, j ]*2^(2^(n-j)), where [ n, j ] is the Gaussian 2-binomial coefficient.

Extensions

a(7)-a(8) from G. C. Greubel, Feb 15 2018