|
%I M3078 N1249 #37 Sep 30 2023 10:50:01
%S 1,3,20,996,9333312,6406603084568576,
%T 16879085743296493582043922521915392,
%U 717956902513121252476003434439730211917452457474409186632352788205535232
%N Number of Post functions of n variables.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D Roger F. Wheeler, Complete propositional connectives. Z. Math. Logik Grundlagen Math. 7, 1961, 185-198.
%H Alois P. Heinz, <a href="/A002857/b002857.txt">Table of n, a(n) for n = 1..12</a>
%H Jürgen Heller, <a href="https://doi.org/10.1016/j.jmp.2016.07.008">Identifiability in probabilistic knowledge structures</a>, J. Math. Psychol. 77, 46-57 (2017).
%H R. F. Wheeler, <a href="/A002543/a002543.pdf">Complete propositional connectives</a>, Z. Math. Logik Grundlagen Math. 7 1961 185-198. [Annotated scanned copy]
%H R. F. Wheeler, <a href="/A002543/a002543_2.pdf">An asymptotic formula for the number of complete propositional connectives</a>, Z. Math. Logik Grundlagen Math. 8 (1962), 1-4. [Annotated scanned copy]
%F Conjecture: a(n) = A055621(n) - A055152(n). - _R. J. Mathar_, Oct 14 2022
%p b:= proc(n, i, l) `if`(n=0, 2^(w-> add(mul(2^igcd(t, l[h]),
%p h=1..nops(l)), t=1..w)/w)(ilcm(l[])), `if`(i<1, 0,
%p add(b(n-i*j, i-1, [l[], i$j])/j!/i^j, j=0..n/i)))
%p end:
%p a:= n-> b(n$2, [])/4:
%p seq(a(n), n=1..8); # _Alois P. Heinz_, Aug 14 2019
%t 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}]]];
%t a[n_] := b[n, n, {}]/4;
%t Array[a, 8] (* _Jean-François Alcover_, Oct 27 2020, after _Alois P. Heinz_ *)
%Y Equals A000612/2 and A003180/4.
%K nonn
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _Vladeta Jovovic_, Feb 23 2000
|
