A002857 Number of Post functions of n variables.

1, 3, 20, 996, 9333312, 6406603084568576, 16879085743296493582043922521915392, 717956902513121252476003434439730211917452457474409186632352788205535232

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

References

• 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).
• Roger F. Wheeler, Complete propositional connectives. Z. Math. Logik Grundlagen Math. 7, 1961, 185-198.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..12
• Jürgen Heller, Identifiability in probabilistic knowledge structures, J. Math. Psychol. 77, 46-57 (2017).
• R. F. Wheeler, Complete propositional connectives, Z. Math. Logik Grundlagen Math. 7 1961 185-198. [Annotated scanned copy]
• R. F. Wheeler, An asymptotic formula for the number of complete propositional connectives, Z. Math. Logik Grundlagen Math. 8 (1962), 1-4. [Annotated scanned copy]

Crossrefs

Equals A000612/2 and A003180/4.

Programs

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-> b(n$2, [])/4:
seq(a(n), n=1..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][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_] := b[n, n, {}]/4;
Array[a, 8] (* Jean-François Alcover, Oct 27 2020, after Alois P. Heinz *)

Formula

Conjecture: a(n) = A055621(n) - A055152(n). - R. J. Mathar, Oct 14 2022

Extensions

More terms from Vladeta Jovovic, Feb 23 2000