login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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).

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 15 18:59 EST 2019. Contains 329149 sequences. (Running on oeis4.)