OFFSET
1,2
COMMENTS
There are two six-pattern sets that are the easiest to avoid, they are identified with one another by either swapping colors (black <-> white) or passing to complements (the latter implies that the compositional inverse e.g.f. F(x) of the sequence in question is -F(-x)). One of them is (in operation notation, with b/w encoding black/white vertices) {b(b(1,2),3), b(b(1,3),2), b(1,b(2,3)), b(w(1,3),2), b(1,w(2,3)), w(b(1,2),3)}, the other is {w(w(1,2),3), w(w(1,3),2), w(1,w(2,3)), w(b(1,3),2), w(1,b(2,3)), b(w(1,2),3)}.
Conjecture: E.g.f. (for offset 0) satisfies A'(x) = 1 + A(x)^3, with A(0)=1. The next terms are 1203498, 24163110, 549811962, 13982486166, 393026414922, ... - Vaclav Kotesovec, Jun 15 2015
REFERENCES
V. Dotsenko, Pattern avoidance in labelled trees, Séminaire Lotharingien de Combinatoire, B67b (2012), 27 pp.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Vladimir Dotsenko, Jul 04 2013
STATUS
approved