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Search: id:A120984
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| A120984 |
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Number of ternary trees with n edges and having no vertices of degree 1. 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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+0
2
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| 1, 0, 3, 1, 18, 15, 138, 189, 1218, 2280, 11826, 27225, 123013, 325611, 1346631, 3919188, 15318342, 47563620, 179405250, 582336054, 2148831144, 7191954822, 26193070008, 89559039141, 323765075223, 1123859351610, 4047466156545
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Column 0 of A120981.
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FORMULA
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a(n)=(1/(n+1)*sum(3^(3j-n)*binomial(n+1,j)*binomial(j,n-2j), j=0..n+1). G.f.=G(z) satisfies G=1+3z^2*G^2+z^3*G^3.
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EXAMPLE
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a(2)=3 because we have (Q,L,M), (Q,L,R) and (Q,M,R), where Q denotes the root and L (M,R) denotes a left (middle, right) child of Q.
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MAPLE
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a:=n->sum(3^(3*j-n)*binomial(n+1, j)*binomial(j, n-2*j), j=0..n+1)/(n+1): seq(a(n), n=0..30);
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CROSSREFS
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Cf. A120981.
Sequence in context: A051141 A068141 A051238 this_sequence A016480 A086156 A147076
Adjacent sequences: A120981 A120982 A120983 this_sequence A120985 A120986 A120987
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 21 2006
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