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Search: id:A127536
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| A127536 |
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Sum of jump-lengths of all even trees with 2n edges. 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 positive difference of the levels is called the jump distance; the sum of the jump distances in a given ordered tree is called the jump-length. |
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+0
3
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| 0, 1, 10, 77, 546, 3740, 25194, 168245, 1118260, 7413705, 49085400, 324794316, 2148789800, 14217578856, 94096891658, 622997471685, 4126520887720, 27345271410275, 181295437422330, 1202538435463365, 7980245606038650
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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a(n)=Sum(k*A127535(n,k),k=0..n-1). The Krandick reference considers jumps and jump-length only in full binary trees.
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REFERENCES
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W. Krandick, Trees and jumps and real roots, J. Computational and Applied Math., 162, 2004, 51-55.
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FORMULA
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a(n)=(n-1)(2n-1)C(3n,n)/[3(n+1)/(2n+1)].
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MAPLE
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seq((n-1)*(2*n-1)*binomial(3*n, n)/3/(n+1)/(2*n+1), n=1..25);
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CROSSREFS
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Cf. A127535, A127533.
Sequence in context: A140763 A081678 A081182 this_sequence A016201 A080618 A082136
Adjacent sequences: A127533 A127534 A127535 this_sequence A127537 A127538 A127539
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 19 2007
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