A127534 Number of jumps in all even trees with 2n edges.

0, 1, 9, 65, 442, 2940, 19380, 127281, 834900, 5476185, 35937525, 236030652, 1551652424, 10210456360, 67254204696, 443410005585, 2926078447656, 19325957314755, 127746785056275, 845069382939705, 5594334252541650

Offset

1,3

Comments

An even tree is an ordered tree in which each vertex has an even outdegree. In the preorder traversal of an ordered tree, any transition from a node at a deeper level to a node on a strictly higher level is called a jump.

The Krandick reference considers jumps in full binary trees.

Links

Table of n, a(n) for n=1..21.

W. Krandick, Trees and jumps and real roots, J. Computational and Applied Math., 162, 2004, 51-55.

Formula

a(n)=(n-1)(4n-3)C(3n,n)/[3(2n+1)(3n-1)].

D-finite with recurrence 8*n*(2*n+1)*a(n) -2*(136*n-69)*(n-1)*a(n-1) +5*(263*n^2-893*n+750)*a(n-2) -156*(3*n-8)*(3*n-10)*a(n-3)=0. - R. J. Mathar, Jul 22 2022

Maple

seq((n-1)*(4*n-3)*binomial(3*n, n)/3/(2*n+1)/(3*n-1), n=1..24);

Mathematica

Table[((n-1)(4n-3)Binomial[3n, n])/(3(2n+1)(3n-1)), {n, 30}] (* Harvey P. Dale, Sep 29 2013 *)

Crossrefs

Cf. A127535, A127536.

Sequence in context: A351530 A081040 A102902 * A037548 A238275 A287816

Adjacent sequences: A127531 A127532 A127533 * A127535 A127536 A127537

Keyword

nonn

Author

Emeric Deutsch, Jan 19 2007

Status

approved