A002857 Number of Post functions of n variables.
1, 3, 20, 996, 9333312, 6406603084568576, 16879085743296493582043922521915392, 717956902513121252476003434439730211917452457474409186632352788205535232
Offset: 1
Keywords
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]
Programs
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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
Extensions
More terms from Vladeta Jovovic, Feb 23 2000