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 A003181 Number of P-equivalence classes of nondegenerate Boolean functions of n variables. (Formerly M0378) 12
 2, 2, 8, 68, 3904, 37329264, 25626412300941056, 67516342973185974302549277749387264, 2871827610052485009904013737758920847602293486924450772201235462734479360 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Also the number of non-isomorphic sets of subsets of {1..n} with union {1..n}. - Gus Wiseman, Aug 05 2019 REFERENCES 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). LINKS Alois P. Heinz, Table of n, a(n) for n = 0..12 S. Muroga, Threshold Logic and Its Applications, Wiley, NY, 1971 [Annotated scans of a few pages] FORMULA a(n) = A003180(n)-A003180(n-1), for n>=1. - Christian Sievers, Jul 22 2016 a(n) = 2 * A055621(n). - Gus Wiseman, Aug 05 2019 EXAMPLE From Gus Wiseman, Aug 05 2019: (Start) 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) MAPLE 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, [])): seq(a(n), n=0..8);  # Alois P. Heinz, Aug 14 2019 MATHEMATICA 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, {}]]; a /@ Range[0, 8] (* Jean-François Alcover, Apr 11 2020, after Alois P. Heinz *) CROSSREFS Cf. A000371, A001146, A003180, A003465, A055621, A007537, A326881. Sequence in context: A053978 A181264 A224766 * A009616 A005615 A048617 Adjacent sequences:  A003178 A003179 A003180 * A003182 A003183 A003184 KEYWORD nonn AUTHOR EXTENSIONS More terms from Christian Sievers, Jul 22 2016 Definition clarified by Ivo Timoteo, Mar 14 2017 STATUS approved

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Last modified June 16 19:49 EDT 2021. Contains 345068 sequences. (Running on oeis4.)