0,1

A003180(n-1) is the number of equivalence classes of Boolean functions of n variables from Post class F(8,inf) under action of symmetric group.

Also number of nonisomorphic sets of subsets of an n-set.

In the 1995 Encyclopedia of Integer Sequences this sequence appears twice, as both M1265 and M3458.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

M. A. Harrison, Introduction to Switching and Automata Theory. McGraw Hill, NY, 1965, p. 147.

S. Muroga, Threshold Logic and Its Applications. Wiley, NY, 1971, p. 38, Table 2.3.2. - Row 5.

Vladeta Jovovic, Table of n, a(n) for n = 0..11

Index entries for sequences related to Boolean functions

a(n) = sum {1*s_1+2*s_2+...=n} (fix A[s_1, s_2, ...]/(1^s_1*s_1!*2^s_2*s_2!*...)) where fix A[s_1, s_2, ...] = 2^sum {i>=1} ( sum {d|i} ( mu(i/d)*( 2^sum {j>=1} ( gcd(j, d)*s_j))))/i.

with(numtheory):with(combinat): for n from 1 to 10 do p:=partition(n): s:=0:for k from 1 to nops(p) do q:=convert(p[k], multiset): for i from 0 to n do a(i):=0:od:for i from 1 to nops(q) do a(q[i][1]):=q[i][2]:od:c:=1:ord:=1:for i from 1 to n do c:=c*a(i)!*i^a(i):ord:=lcm(ord, i):od: ss:=0:for i from 1 to ord do if ord mod i=0 then ss:=ss+phi(ord/i)*2^add(gcd(j, i)*a(j), j=1..n):fi:od: s:=s+2^(ss/ord)/c:od: printf(`%d `, n):printf("%d ", s):od: - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 19 2006

a(n) = 2*A000612(n). Cf. A001146.

Sequence in context: A141522 A114903 A038054 this_sequence A002080 A001206 A144295

Adjacent sequences: A003177 A003178 A003179 this_sequence A003181 A003182 A003183

nonn,nice

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Jovovic Vladeta (vladeta(AT)eunet.rs)

Edited with formula by Christian G. Bower (bowerc(AT)usa.net), Jan 08 2004