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 A179176 Number of vertices with even distance from the root in "0-1-2" 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 (list; graph; refs; listen; history; text; internal format)
 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 FORMULA G.f.: (M*T^2)/(2T-1) where M =(1-z-sqrt(1-2*z-3*z^2))/(2*z^2), the g.f. for the Motzkin numbers, and T=1/sqrt(1-2*z-3*z^2), the g.f. for the central trinomial numbers. Conjecture: 3*(n+2)*(2*n-1)*a(n) -(4*n+5)*(2*n-1)*a(n-1) +(-20*n^2-8*n+27)*a(n-2) -3*(2*n+3)*(4*n-3)*a(n-3) -9*(2*n+3)*(n-1)*a(n-4)=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 "0-1-2" 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

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Last modified December 9 00:32 EST 2019. Contains 329871 sequences. (Running on oeis4.)