A224766
Number of non-degenerate fanout-free Boolean functions of n variables using And, Or and Not gates.
Original entry on oeis.org
2, 2, 8, 64, 832, 15104, 352256, 10037248, 337936384, 13126565888, 577818263552, 28425821618176, 1545553369366528, 92034646352592896, 5956917762776367104, 416397789920380321792, 31262503202358260924416, 2508985620606225641111552, 214348807882902869374926848
Offset: 0
- J. P. Hayes, Enumeration of fanout-free Boolean functions, J. ACM, 23 (1976), 700-709.
A225170
Number of non-degenerate fanout-free Boolean functions of n variables having AND rank 1.
Original entry on oeis.org
2, 4, 32, 416, 7552, 176128, 5018624, 168968192, 6563282944, 288909131776, 14212910809088, 772776684683264, 46017323176296448, 2978458881388183552, 208198894960190160896, 15631251601179130462208, 1254492810303112820555776, 107174403941451434687463424
Offset: 1
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max = 16; s = -ProductLog[-Exp[x-1/2]/2] + O[x]^max; Join[{2}, Drop[CoefficientList[s, x]*Range[0, max-1]!, 2]] (* Jean-François Alcover, Oct 18 2016 *)
a[1] = 2; a[n_] := (Sum[(n + k - 1)!*Sum[(-1)^j/(k - j)!*Sum[(-1)^i*2^(n - i + j - 1)*StirlingS1[n - i + j - 1, j - i]/((n - i + j - 1)!*i!), {i, 0, j}], {j, 1, k}], {k, 1, n - 1}]);
Array[a, 20] (* Jean-François Alcover, Jun 24 2018, after Vladimir Kruchinin *)
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seq(n) = Vec(serlaplace(serreverse((1 + 2*x - exp(x + O(x*x^n)))/2 ))) \\ Andrew Howroyd, Mar 28 2025
A005756
Number of non-degenerate fanout-free Boolean functions of n variables having AND rank 2.
Original entry on oeis.org
4, 24, 304, 5440, 125824, 3566080, 119614464, 4633387008, 203524112384, 9995546722304, 542730361241600, 32281981804347392, 2087454641985945600, 145797871819529650176, 10938609224992417644544, 877346430770422497673216, 74913579745878635293179904, 6784650500440844952024383488
Offset: 2
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
A224767
Number of non-degenerate fanout-free Boolean functions of n variables having AND rank 3.
Original entry on oeis.org
8, 96, 1760, 41280, 1180928, 39875584, 1552320512, 68449628160, 3372052676608, 183551641878528, 10940489276194816, 708687880636596224, 49572421008089939968, 3724036897414481707008, 299029855691955400343552, 25558593192866693643239424, 2316797640852393238300983296
Offset: 3
- J. P. Hayes, Enumeration of fanout-free Boolean functions, J. ACM, 23 (1976), 700-709.
A224768
Number of non-degenerate fanout-free Boolean functions of n variables having AND rank 4.
Original entry on oeis.org
16, 320, 8000, 237440, 8212736, 325183488, 14520770560, 722332835840, 39624284553216, 2376711326466048, 154762773034827776, 10873462063657123840, 819935630669686767616, 66053636326538996613120, 5661819237475388709928960, 514513306050639489811873792, 49411385426075987313590009856
Offset: 4
- J. P. Hayes, Enumeration of fanout-free Boolean functions, J. ACM, 23 (1976), 700-709.
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