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A227250 Number of binary labeled trees with two-colored vertices that have n leaves and avoid the easiest to avoid 6-pattern set. 1
1, 2, 6, 42, 390, 4698, 69174 (list; graph; refs; listen; history; text; internal format)



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


V. Dotsenko, Pattern avoidance in labelled trees, Séminaire Lotharingien de Combinatoire, B67b (2012), 27 pp.


Table of n, a(n) for n=1..7.


Cf. A258880, A258969.

Sequence in context: A074015 A074021 A050862 * A258969 A161632 A115974

Adjacent sequences:  A227247 A227248 A227249 * A227251 A227252 A227253




Vladimir Dotsenko, Jul 04 2013



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Last modified January 19 21:47 EST 2020. Contains 331066 sequences. (Running on oeis4.)