login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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