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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 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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