A002857 -id:A002857 - cp's OEIS frontend

A002543 Complete Post functions of n variables.

Original entry on oeis.org

0, 2, 16, 980, 9332768

Offset: 1

N. J. A. Sloane

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).
Wheeler, Roger F.; Complete propositional connectives. Z. Math. Logik Grundlagen Math. 7 1961 185-198.
Wheeler, Roger F.; Complete connectives for the 3-valued propositional calculus. Proc. London Math. Soc. (3) 16 1966 167-191.

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]
R. F. Wheeler, Complete connectives for the 3-valued propositional calculus, Proc. London Math. Soc. (3) 16 (1966), 167-191. [Annotated scanned copy]

Cf. A002542, A002857.

A055152 Proper covers of an unlabeled n-set.

Original entry on oeis.org

0, 1, 14, 956, 9331320, 6406603065901952, 16879085743296493569230716352778240, 717956902513121252476003434439730211883694285987816199468264943161704448

Offset: 1

Vladeta Jovovic, Jun 14 2000

Alois P. Heinz, Table of n, a(n) for n = 1..12
Heller, Jürgen Identifiability in probabilistic knowledge structures. J. Math. Psychol. 77, 46-57 (2017).
Eric Weisstein's World of Mathematics, Proper covers

See A007537 for labeled case. Cf. A055621.

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, [])-2*b(n-1$2, []))/4:
seq(a(n), n=1..8);  # Alois P. Heinz, Aug 14 2019

b[n_] := Sum[1/Function[p, Product[Function[c, j^c*c!][Coefficient[p, x, j]], {j, 1, Exponent[p, x]}]][Total[x^l]]*2^(Function[w, Sum[Product[ 2^GCD[t, l[[i]]], {i, 1, Length[l]}], {t, 1, w}]/w][If[l == {}, 1, LCM @@ l]]), {l, IntegerPartitions[n]}];
a[n_] := (b[n] - 2 b[n - 1])/4;
a /@ Range[8] (* Jean-François Alcover, Feb 19 2020, after Alois P. Heinz in A000612 *)

a(n) = (A003180(n) - 2*A003180(n-1))/4.

Apparently a(n) = A002857(n) - A000612(n-1). - R. J. Mathar, Apr 22 2007

More terms from David Wasserman, Mar 21 2002

A262546 Number of Post functions of n variables which fail to satisfy Post's second condition.

Original entry on oeis.org

1, 1, 4, 16, 544

Offset: 1

N. J. A. Sloane, Oct 06 2015

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]

Equals A002857 - A002543.

A262547 Nearest integer to 2^(2^n)/(4*n!).

Original entry on oeis.org

1, 2, 11, 683, 8947849, 6405119470038039, 16879085660760836481318184892448820, 717956902513121251386228825698709746114025202539934052824017757985572480

Offset: 1

N. J. A. Sloane, Oct 06 2015

nonn

Jon E. Schoenfield, Table of n, a(n) for n = 1..11
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]

An approximation to A002857.

cp's OEIS Frontend

A002543 Complete Post functions of n variables.

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A055152 Proper covers of an unlabeled n-set.

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A262546 Number of Post functions of n variables which fail to satisfy Post's second condition.

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A262547 Nearest integer to 2^(2^n)/(4*n!).

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