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A120985
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Number of ternary trees with n edges and having no vertices of degree 2. A ternary tree is a rooted tree in which each vertex has at most three children and each child of a vertex is designated as its left or middle or right child.
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1
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1, 3, 9, 28, 93, 333, 1272, 5085, 20925, 87735, 372879, 1602450, 6953824, 30438138, 134255403, 596154495, 2662813341, 11955684591, 53927330037, 244250703252, 1110401393067, 5065143385647, 23176155530394, 106344639962973
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Column 0 of A120982.
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FORMULA
| a(n)=(1/(n+1))*sum(3^(n-3j)*binomial(n+1,2j+1)*binomial(n-2j,j), j=0..n/2). G.f.=G(z) satisfies G=1+3zG + z^3*G^3.
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EXAMPLE
| a(1)=3 because we have (Q,L), (Q,M) and (Q,R), where Q denotes the root and L (M,R) denotes a left (middle, right) child of Q.
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MAPLE
| a:=n->sum(3^(n-3*j)*binomial(n+1, 2*j+1)*binomial(n-2*j, j), j=0..n/2)/(n+1): seq(a(n), n=0..27);
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CROSSREFS
| Cf. A120982.
Sequence in context: A131203 A191637 A081914 * A014323 A000752 A047027
Adjacent sequences: A120982 A120983 A120984 * A120986 A120987 A120988
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 21 2006
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