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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

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

LINKS

Table of n, a(n) for n=0..27.

Gi-Sang Cheon and Louis W. Shapiro, Protected points in ordered trees, Appl. Math. Letters, 21, 2008, 516-520.

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^3-2z(1+z)G^2+(1+3z+z^2)G-(1+2z)=0.

MAPLE

p:=z^2*G^3-2*z*G^2-2*z^2*G^2+3*z*G+G+z^2*G-1-2*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

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Last modified January 22 23:50 EST 2022. Contains 350504 sequences. (Running on oeis4.)