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A003181
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Number of P-equivalence classes of nondegenerate Boolean functions of n variables.
(Formerly M0378)
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12
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OFFSET
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0,1
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COMMENTS
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Also the number of non-isomorphic sets of subsets of {1..n} with union {1..n}. - Gus Wiseman, Aug 05 2019
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REFERENCES
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S. Muroga, Threshold Logic and Its Applications. Wiley, NY, 1971, p. 38 and 214.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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EXAMPLE
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Non-isomorphic representatives of the a(0) = 2 through a(2) = 8 sets of subsets:
{} {{1}} {{1,2}}
{{}} {{},{1}} {{1},{2}}
{{},{1,2}}
{{2},{1,2}}
{{},{1},{2}}
{{},{2},{1,2}}
{{1},{2},{1,2}}
{{},{1},{2},{1,2}}
(End)
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MAPLE
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b:= proc(n, i, l) `if`(n=0, 2^(w-> add(mul(2^igcd(t, l[h]),
h=1..nops(l)), t=1..w)/w)(ilcm(l[])), `if`(i<1, 0,
add(b(n-i*j, i-1, [l[], i$j])/j!/i^j, j=0..n/i)))
end:
a:= n-> `if`(n=0, 2, b(n$2, [])-b(n-1$2, [])):
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MATHEMATICA
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b[n_, i_, l_] := If[n == 0, 2^Function[w, Sum[Product[2^GCD[t, l[[h]]], {h, 1, Length[l]}], {t, 1, w}]/w][If[l == {}, 1, LCM @@ l]], If[i < 1, 0, Sum[b[n - i*j, i - 1, Join[l, Table[i, {j}]]]/j!/i^j, {j, 0, n/i}]]];
a[n_] := If[n == 0, 2, b[n, n, {}] - b[n - 1, n - 1, {}]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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