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A178834
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a(n) counts anti-chains of size two in "0,1,2" Motzkin trees on n edges
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1
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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
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OFFSET
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0,4
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COMMENTS
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"0,1,2" trees are rooted trees where each vertex has out degree zero, one or two. They are counted by the Motzkin numbers.
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LINKS
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Table of n, a(n) for n=0..25.
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FORMULA
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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
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EXAMPLE
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For n=3 we have a(3)=5, there are 5 two element anti-chains on "0,1,2" Motzkin trees on 3 edges.
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PROG
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(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
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CROSSREFS
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Sequence in context: A147359 A034447 A121329 * A146013 A028894 A140529
Adjacent sequences: A178831 A178832 A178833 * A178835 A178836 A178837
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KEYWORD
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nonn
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AUTHOR
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Lifoma Salaam, Dec 27 2010
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STATUS
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approved
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