A218093 Number of transitive reflexive early confluent binary relations R on n labeled elements with max_{x}(|{y : xRy}|) = 3.

13, 106, 1105, 12075, 141533, 1812216, 25188019, 378725365, 6135529675, 106586385708, 1976799958367, 38978490654831, 814024466784025, 17943457752971680, 416183933276776375, 10128962147830237953, 258021086313431979827, 6863916836407264864380

Offset

3,1

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 = 3..200

Formula

E.g.f.: exp(x*exp(x*exp(x)+x^2/2)+x^2/2*exp(x)+x^3/6)-exp(x*exp(x)+x^2/2).

a(n) = A210911(n) - A135312(n).

Maple

egf:= exp(x*exp(x*exp(x)+x^2/2)+x^2/2*exp(x)+x^3/6)-exp(x*exp(x)+x^2/2):
a:= n-> n!* coeff(series(egf, x, n+1), x, n):
seq(a(n), n=3..30);

Crossrefs

Column k=3 of A135313.

Sequence in context: A055902 A295249 A295648 * A132261 A142364 A164301

Adjacent sequences: A218090 A218091 A218092 * A218094 A218095 A218096

Keyword

nonn

Author

Alois P. Heinz, Oct 20 2012

Status

approved