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A120985 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. 2
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; text; internal format)
OFFSET

0,2

COMMENTS

Column 0 of A120982.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..300

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.

Recurrence: 2*n*(2*n+3)*a(n) = 6*(6*n^2-1)*a(n-1) - 54*(n-1)*(2*n-1)*a(n-2) + 135*(n-2)*(n-1)*a(n-3). - Vaclav Kotesovec, Oct 19 2012

a(n) ~ (3+3/2^(2/3))^(n+3/2)/(2*sqrt(3*Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 19 2012

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.

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);

MATHEMATICA

Table[1/(n+1)*Sum[3^(n-3*j)*Binomial[n+1, 2*j+1]*Binomial[n-2*j, j], {j, 0, n/2}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 19 2012 *)

CROSSREFS

Cf. A120982.

Sequence in context: A191637 A238978 A081914 * A014323 A000752 A047027

Adjacent sequences:  A120982 A120983 A120984 * A120986 A120987 A120988

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Jul 21 2006

STATUS

approved

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Last modified February 25 05:47 EST 2020. Contains 332220 sequences. (Running on oeis4.)