A218095 Number of transitive reflexive early confluent binary relations R on n labeled elements with max_{x}(|{y : xRy}|) = 5.

541, 11301, 239379, 5287506, 124878033, 3151808478, 84934607175, 2440299822081, 74564772630777, 2416548374532292, 82847673438018762, 2996998457878842144, 114123931204449050115, 4564365783126801549858, 191334572138628994076241, 8390237730288860299836005

Offset: 5

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 = 5..200

Crossrefs

Column k=5 of A135313.

Programs

Maple

t:= proc(k) option remember; `if`(k<0, 0,
      unapply(exp(add(x^m/m! *t(k-m)(x), m=1..k)), x))
    end:
egf:= t(5)(x)-t(4)(x):
a:= n-> n!* coeff(series(egf, x, n+1), x, n):
seq(a(n), n=5..20);

Mathematica

m = 5; t[k_] := t[k] = If[k<0, 0, Function[x, Exp[Sum[x^m/m!*t[k-m][x], {m, 1, k}]]]] ; egf = t[m][x]-t[m-1][x]; a[n_] := n!*Coefficient[Series[egf, {x, 0, n+1}], x, n]; Table[a[n], {n, m, 20}] (* Jean-François Alcover, Feb 14 2014, after Maple *)

Formula

E.g.f.: t_5(x)-t_4(x), with t_k(x) = exp (Sum_{m=1..k} x^m/m! * t_{k-m}(x)) if k>=0 and t_k(x) = 0 else.

a(n) = A210913(n) - A210912(n).