

A121447


Level of the first leaf (in preorder traversal) of a ternary tree, summed over all ternary trees with n edges. 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



3, 21, 127, 747, 4386, 25897, 154077, 923910, 5581485, 33949836, 207787668, 1278900412, 7911394686, 49165322241, 306809507561, 1921849861260, 12079999018605, 76170034283805, 481680300300255, 3054157623774495
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OFFSET

1,1


COMMENTS

a(n)=Sum(k*A121445(n,k),k=1..n).


LINKS

Table of n, a(n) for n=1..20.


FORMULA

a(n)=3n(23n^2+78n+67)binomial(3n+2,n+2)/[4(n+3)(2n+1)(2n+3)(2n+5)]. G.f.= (h1z)(h1)/z^2, where h=1+zh^3=2sin(arcsin(sqrt(27z/4))/3)/sqrt(3z).


EXAMPLE

a(1)=3 because each of the trees /,  and \ contributes 1 to the sum.


MAPLE

a:=n>3*n*(23*n^2+78*n+67)*binomial(3*n+2, n+2)/4/(n+3)/(2*n+1)/(2*n+3)/(2*n+5): seq(a(n), n=1..23);


CROSSREFS

Cf. A121455.
Sequence in context: A220616 A273803 A036754 * A125682 A125701 A274586
Adjacent sequences: A121444 A121445 A121446 * A121448 A121449 A121450


KEYWORD

nonn


AUTHOR

Emeric Deutsch, Jul 30 2006


STATUS

approved



