

A178834


a(n) counts antichains 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
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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 =(1zsqrt(12*z3*z^2))/(2*z^2) the Motzkin numbers and T=1/sqrt(12*z3*z^2) the Central Trinomial numbers
Conjecture: (n2)*(n+2)*a(n) +(4*n^2n8)*a(n1) +(2*n^2n12)*a(n2) 3*n*(4*n3)*a(n3) 9*n*(n1)*a(n4)=0.  R. J. Mathar, Jun 14 2016


EXAMPLE

For n=3 we have a(3)=5, there are 5 two element antichains on "0,1,2" Motzkin trees on 3 edges.


PROG

(PARI) z='z+O('z^33); M=(1zsqrt(12*z3*z^2))/(2*z^2); T=1/sqrt(12*z3*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



