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

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

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: A034447 A121329 A246175 * 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 November 28 00:22 EST 2014. Contains 250286 sequences.