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A003180 Number of equivalence classes of Boolean functions of n variables under action of symmetric group.
(Formerly M1265 N1405)
+0
8
2, 4, 12, 80, 3984, 37333248, 25626412338274304, 67516342973185974328175690087661568, 2871827610052485009904013737758920847669809829897636746529411152822140928 (list; graph; listen)
OFFSET

0,1

COMMENT

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.

REFERENCES

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.

LINKS

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

Index entries for sequences related to Boolean functions

FORMULA

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.

MAPLE

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.yu), Sep 19 2006

CROSSREFS

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

Sequence in context: A060935 A114903 A038054 this_sequence A002080 A001206 A119489

Adjacent sequences: A003177 A003178 A003179 this_sequence A003181 A003182 A003183

KEYWORD

nonn,nice

AUTHOR

njas

EXTENSIONS

More terms from Jovovic Vladeta (vladeta(AT)Eunet.yu)

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

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Last modified August 19 23:53 EDT 2008. Contains 142930 sequences.


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