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 A000612 Number of P-equivalence classes of switching functions of n or fewer variables, divided by 2. (Formerly M1712 N0677) 62
 1, 2, 6, 40, 1992, 18666624, 12813206169137152, 33758171486592987164087845043830784, 1435913805026242504952006868879460423834904914948818373264705576411070464 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Also nonisomorphic sets of nonempty subsets of an n-set. REFERENCES M. A. Harrison, Introduction to Switching and Automata Theory. McGraw Hill, NY, 1965, p. 153. S. Muroga, Threshold Logic and Its Applications. Wiley, NY, 1971, p. 38 Table 2.3.2. - Row 5. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). 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 M. A. Harrison, The number of equivalence classes of Boolean functions under groups containing negation, IEEE Trans. Electron. Comput. 12 (1963), 559-561. M. A. Harrison, The number of equivalence classes of Boolean functions under groups containing negation, IEEE Trans. Electron. Comput. 12 (1963), 559-561. [Annotated scanned copy] EXAMPLE Non-isomorphic representatives of the a(2) = 6 set-systems are 0, {1}, {12}, {1}{2}, {1}{12}, {1}{2}{12}. - Gus Wiseman, Aug 07 2018 MAPLE a:= n-> add(1/(p-> mul((c-> j^c*c!)(coeff(p, x, j)), j=1..degree(p)))(         add(x^i, i=l))*2^((w-> add(mul(2^igcd(t, l[i]), i=1..nops(l)),         t=1..w)/w)(ilcm(l[]))), l=combinat[partition](n))/2: seq(a(n), n=0..9);  # Alois P. Heinz, Aug 12 2019 MATHEMATICA sysnorm[{}] := {}; sysnorm[m_]:=If[Union@@m!=Range[Max@@Flatten[m]], sysnorm[m/.Rule@@@Table[{(Union@@m)[[i]], i}, {i, Length[Union@@m]}]], First[Sort[sysnorm[m, 1]]]]; sysnorm[m_, aft_]:=If[Length[Union@@m]<=aft, {m}, With[{mx=Table[Count[m, i, {2}], {i, Select[Union@@m, #>=aft&]}]}, Union@@(sysnorm[#, aft+1]&/@Union[Table[Map[Sort, m/.{par+aft-1->aft, aft->par+aft-1}, {0, 1}], {par, First/@Position[mx, Max[mx]]}]])]]; Table[Length[Union[sysnorm/@Subsets[Rest[Subsets[Range[n]]]]]], {n, 4}] (* Gus Wiseman, Aug 07 2018 *) a[n_] := Sum[1/Function[p, Product[Function[c, j^c*c!][Coefficient[p, x, j]], {j, 1, Exponent[p, x]}]][Total[x^l]]*2^(Function[w, Sum[Product[2^GCD[t, l[[i]]], {i, 1, Length[l]}], {t, 1, w}]/w][If[l=={}, 1, LCM @@ l]]), {l, IntegerPartitions[n]}]/2; a /@ Range[0, 9] (* Jean-François Alcover, Feb 04 2020, after Alois P. Heinz *) CROSSREFS a(n) = A003180(n)/2. Cf. A007716, A055621, A058891, A283877, A300913, A306005, A317533, A317757. Sequence in context: A135755 A051185 A118623 * A319633 A326268 A096138 Adjacent sequences:  A000609 A000610 A000611 * A000613 A000614 A000615 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS More terms from Vladeta Jovovic, Feb 23 2000 STATUS approved

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Last modified March 31 03:48 EDT 2020. Contains 333136 sequences. (Running on oeis4.)