

A179176


Number of vertices with even distance from the root in "012" Motzkin trees on n edges.


0



1, 1, 3, 9, 24, 66, 187, 529, 1506, 4312, 12394, 35742, 103377, 299745, 871011, 2535873, 7395522, 21600720, 63176964, 185004852, 542365407, 1591631595, 4675170690, 13744341390, 40438307599, 119063564395, 350799321531
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OFFSET

0,3


COMMENTS

"0,1,2" trees are rooted trees where each vertex has out degree zero, one, or two. They are counted by the Motzkin numbers.


LINKS

Table of n, a(n) for n=0..26.


FORMULA

G.f.: (M*T^2)/(2T1) where M =(1zsqrt(12*z3*z^2))/(2*z^2), the g.f. for the Motzkin numbers, and T=1/sqrt(12*z3*z^2), the g.f. for the central trinomial numbers.
Conjecture: 3*(n+2)*(2*n1)*a(n) (4*n+5)*(2*n1)*a(n1) +(20*n^28*n+27)*a(n2) 3*(2*n+3)*(4*n3)*a(n3) 9*(2*n+3)*(n1)*a(n4)=0.  R. J. Mathar, Jul 24 2012


EXAMPLE

We have a(3)=9, as there are 9 vertices with even distance from the root in the 4 "012" Motzkin trees on 3 edges.


CROSSREFS

Cf. A178834, A121320, A091958, A143364, A091958
Sequence in context: A096168 A051042 A121907 * A118771 A091587 A316892
Adjacent sequences: A179173 A179174 A179175 * A179177 A179178 A179179


KEYWORD

nonn


AUTHOR

Lifoma Salaam, Jan 04 2011


STATUS

approved



