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.

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

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.= (h-1-z)(h-1)/z^2, where h=1+zh^3=2sin(arcsin(sqrt(27z/4))/3)/sqrt(3z).

D-finite with recurrence -2*(2*n+5)*(n+3)*(1951*n-2094)*a(n) +(43553*n^3+142716*n^2+115045*n-10338)*a(n-1) +3*(2281*n+1723)*(3*n-1)*(3*n-2)*a(n-2)=0. - R. J. Mathar, Jul 24 2022

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 A357783 A360626

Adjacent sequences: A121444 A121445 A121446 * A121448 A121449 A121450

Keyword

nonn

Author

Emeric Deutsch, Jul 30 2006

Status

approved