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A127534
Number of jumps in all even trees with 2n edges.
0
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
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
Sequence in context: A351530 A081040 A102902 * A037548 A238275 A287816
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Jan 19 2007
STATUS
approved