

A143363


Number of ordered trees with n edges and having no protected vertices. A protected vertex in an ordered tree is a vertex at least 2 edges away from its leaf descendants.


6



1, 1, 1, 3, 6, 17, 43, 123, 343, 1004, 2938, 8791, 26456, 80597, 247091, 763507, 2372334, 7413119, 23271657, 73376140, 232238350, 737638868, 2350318688, 7510620143, 24064672921, 77294975952, 248832007318, 802737926643
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OFFSET

0,4


COMMENTS

The "no protected vertices" condition can be rephrased as "every nonleaf vertex has at least one leaf child". But a(n) is also the number of ordered trees with n edges in which every nonleaf vertex has at most one leaf child. [David Callan, Aug 22 2014]


LINKS

Table of n, a(n) for n=0..27.
GiSang Cheon and Louis W. Shapiro, Protected points in ordered trees, Appl. Math. Letters, 21, 2008, 516520.
Murray Tannock, Equivalence classes of mesh patterns with a dominating pattern, MSc Thesis, Reykjavik Univ., May 2016.


FORMULA

a(n) = A143362(n,0) for n>=1.
G.f.=G=G(z) satisfies z^2*G^32z(1+z)G^2+(1+3z+z^2)G(1+2z)=0.


MAPLE

p:=z^2*G^32*z*G^22*z^2*G^2+3*z*G+G+z^2*G12*z=0: G:=RootOf(p, G): Gser:= series(G, z=0, 33): seq(coeff(Gser, z, n), n=0..28);


CROSSREFS

Cf. A143362.
Sequence in context: A238428 A232771 A129905 * A216878 A237670 A321227
Adjacent sequences: A143360 A143361 A143362 * A143364 A143365 A143366


KEYWORD

nonn


AUTHOR

Emeric Deutsch, Aug 20 2008


STATUS

approved



