A002857 Number of Post functions of n variables. (Formerly M3078 N1249)

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

Offset

1,2

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]

Formula

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

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 *)

Crossrefs

Equals A000612/2 and A003180/4.

Sequence in context: A108699 A162134 A296408 * A345328 A203314 A174652

Adjacent sequences: A002854 A002855 A002856 * A002858 A002859 A002860

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Vladeta Jovovic, Feb 23 2000

Status

approved