A218092 Number of transitive reflexive early confluent binary relations R on n labeled elements with max_{x}(|{y : xRy}|) = 2.

3, 12, 61, 310, 1821, 11592, 80963, 608832, 4910785, 42159238, 383478987, 3678859158, 37087880753, 391641822540, 4319860660447, 49647399946048, 593217470459313, 7354718987639958, 94445777492433515, 1254196823154143190, 17198114810490326713

Offset: 2

Author

Alois P. Heinz, Oct 20 2012

Keywords

• nonn

Comments

R is early confluent iff (xRy and xRz) implies (yRz or zRy) for all x, y, z.

References

• A. P. Heinz (1990). Analyse der Grenzen und Möglichkeiten schneller Tableauoptimierung. PhD Thesis, Albert-Ludwigs-Universität Freiburg, Freiburg i. Br., Germany.

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..200

Crossrefs

Column k=2 of A135313.

Programs

Maple

egf:= exp(x*exp(x)+x^2/2)-exp(x):
a:= n-> n!* coeff(series(egf, x, n+1), x, n):
seq(a(n), n=2..30);

Mathematica

nn=22; Drop[CoefficientList[Series[Exp[x Exp[x]+x^2/2]-Exp[x],{x,0,nn}],x] Range[0,nn]!,2] (* Harvey P. Dale, May 03 2014 *)

Formula

E.g.f.: exp(x*exp(x)+x^2/2)-exp(x).

a(n) = A135312(n) - A000012(n).