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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

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Last modified October 24 09:28 EDT 2014. Contains 248516 sequences.