|
| |
|
|
A120984
|
|
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.
|
|
1
| |
|
|
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; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| Column 0 of A120981.
|
|
|
FORMULA
| 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.
|
|
|
EXAMPLE
| 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.
|
|
|
MAPLE
| 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);
|
|
|
CROSSREFS
| Cf. A120981.
Sequence in context: A051141 A068141 A051238 * A016480 A086156 A188109
Adjacent sequences: A120981 A120982 A120983 * A120985 A120986 A120987
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 21 2006
|
| |
|
|
