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

 

Logo

Invitation: celebrating 50 years of OEIS, 250000 sequences, and Sloane's 75th, there will be a conference at DIMACS, Rutgers, Oct 9-10 2014.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A178834 a(n) counts anti-chains of size two in "0,1,2" Motzkin trees on n edges 1
0, 0, 1, 5, 23, 91, 341, 1221, 4249, 14465, 48442, 160134, 523872, 1699252, 5472713, 17520217, 55801733, 176942269, 558906164, 1759436704, 5522119250, 17285351782, 53977433618, 168194390290, 523076690018, 1623869984706 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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..25.

FORMULA

G.f.: z^2*M^2*T^3 where M =(1-z-sqrt(1-2*z-3*z^2))/(2*z^2) the Motzkin numbers and T=1/sqrt(1-2*z-3*z^2) the Central Trinomial numbers

EXAMPLE

For n=3 we have a(3)=5, there are 5 two element anti-chains on "0,1,2" Motzkin trees on 3 edges.

PROG

(PARI) z='z+O('z^33); M=(1-z-sqrt(1-2*z-3*z^2))/(2*z^2); T=1/sqrt(1-2*z-3*z^2); v=Vec(z^2*M^2*T^3+'tmp); v[1]=0; v

CROSSREFS

Sequence in context: A147359 A034447 A121329 * A146013 A028894 A140529

Adjacent sequences:  A178831 A178832 A178833 * A178835 A178836 A178837

KEYWORD

nonn

AUTHOR

Lifoma Salaam, Dec 27 2010

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified July 31 00:52 EDT 2014. Contains 245078 sequences.