The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A002857 Number of Post functions of n variables. (Formerly M3078 N1249) 5
 1, 3, 20, 996, 9333312, 6406603084568576, 16879085743296493582043922521915392, 717956902513121252476003434439730211917452457474409186632352788205535232 (list; graph; refs; listen; history; text; internal format)
 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). Wheeler, Roger F.; 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 EXTENSIONS More terms from Vladeta Jovovic, Feb 23 2000 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 7 12:27 EST 2022. Contains 358656 sequences. (Running on oeis4.)