A218097 Number of transitive reflexive early confluent binary relations R on n labeled elements with max_{x}(|{y : xRy}|) = 7.

47293, 1863044, 64432638, 2185028130, 75967708311, 2755081426548, 104970367609107, 4210378306984993, 177779119899659850, 7894403946290257968, 368141001305925742232, 17999569547430255114096, 921163485872922579361467, 49262708358493465135411860

Offset

7,1

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 = 7..200

Formula

E.g.f.: t_7(x)-t_6(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) = A210915(n) - A210914(n).

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(7)(x)-t(6)(x):
a:= n-> n!* coeff(series(egf, x, n+1), x, n):
seq(a(n), n=7..22);

Mathematica

m = 7; 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 *)

Crossrefs

Column k=7 of A135313.

Sequence in context: A215840 A257723 A320621 * A293584 A263067 A234708

Adjacent sequences: A218094 A218095 A218096 * A218098 A218099 A218100

Keyword

nonn

Author

Alois P. Heinz, Oct 20 2012

Status

approved