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Search: id:A127533
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| A127533 |
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Sum of jump-lengths of all binary trees with n edges. In the preorder traversal of a binary 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 binary tree is called the jump-length. |
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+0
3
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| 0, 0, 0, 2, 17, 100, 506, 2366, 10556, 45696, 193800, 810084, 3350479, 13748020, 56071470, 227613750, 920540040, 3711935040, 14932102320, 59951235420, 240316859250, 962056169256, 3847193657076, 15370712686252, 61364157982952
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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a(n)=Sum(A127532(n,k),k>=0). The Krandick reference is about jumps and jump-length 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)=C(2n+1,n-3)+C(2n,n-3). G.f.=z^3*C^6*(C+1)/sqrt(1-4z), where C=[1-sqrt(1-4z)]/(2z) is the Catalan function.
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MAPLE
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seq(binomial(2*n+1, n-3)+binomial(2*n, n-3), n=0..28);
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CROSSREFS
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Cf. A127532, A127529.
Sequence in context: A100268 A129123 A109724 this_sequence A023260 A119363 A129977
Adjacent sequences: A127530 A127531 A127532 this_sequence A127534 A127535 A127536
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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 18 2007
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