A218099 Number of transitive reflexive early confluent binary relations R on n labeled elements with max_{x}(|{y : xRy}|) = 9.

7087261, 451238935, 22913136730, 1087116745385, 51075201835515, 2437976801668408, 119752042470064290, 6093096859120003590, 322215964319093498225, 17735784941946000072572, 1016521929886047797022408, 60650840653136697085038930, 3764766650086543657134295955

Offset: 9

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 = 9..200

Crossrefs

Column k=9 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(9)(x)-t(8)(x):
a:= n-> n!* coeff(series(egf, x, n+1), x, n):
seq(a(n), n=9..22);

Mathematica

m = 9; 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, 22}] (* Jean-François Alcover, Feb 14 2014, after Maple *)

Formula

E.g.f.: t_9(x)-t_8(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) = A210917(n) - A210916(n).