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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

Conjecture: -(n-2)*(n+2)*a(n) +(4*n^2-n-8)*a(n-1) +(2*n^2-n-12)*a(n-2) -3*n*(4*n-3)*a(n-3) -9*n*(n-1)*a(n-4)=0. - R. J. Mathar, Jun 14 2016

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: A121329 A246175 A283224 * A255457 A146013 A028894

Adjacent sequences:  A178831 A178832 A178833 * A178835 A178836 A178837

KEYWORD

nonn

AUTHOR

Lifoma Salaam, Dec 27 2010

STATUS

approved

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Last modified August 23 09:50 EDT 2017. Contains 290986 sequences.