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Search: id:A101308
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| A101308 |
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Number of ordered trees with n edges and having no branches of length 2. |
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+0
2
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| 1, 1, 1, 3, 7, 18, 47, 129, 362, 1038, 3022, 8917, 26600, 80098, 243132, 743180, 2285597, 7067271, 21957947, 68517606, 214633572, 674712991, 2127790260, 6729876378, 21342679122, 67851885121, 216204228642, 690371596017
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Column 0 of the triangle A101307.
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REFERENCES
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E. Deutsch, Ordered trees with prescribed root degrees, node degrees, and branch lengths, Discrete Math., 282, 2004, 89-94.
J. Riordan, Enumeration of plane trees by branches and endpoints, J. Comb. Theory (A) 19, 1975, 214-222.
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FORMULA
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G.f.=[1-z^2+z^3-sqrt[(1-z^2+z^3)(1-4z+3z^2-3z^3)]]/[2z(1-z+z^2)].
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EXAMPLE
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a(3)=3 because we have:(i) a path of length tree hanging from the root, (ii) an edge hanging from the root, from the end of which two edges are hanging, and (iii) three edges hanging from the root.
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MAPLE
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G:=(1-z^2+z^3-sqrt((1-z^2+z^3)*(1-4*z+3*z^2-3*z^3)))/2/z/(1-z+z^2): Gser:=series(G, z=0, 34): 1, seq(coeff(Gser, z^n), n=1..32);
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CROSSREFS
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Cf. A101307.
Sequence in context: A027971 A018028 A045994 this_sequence A018029 A099483 A103177
Adjacent sequences: A101305 A101306 A101307 this_sequence A101309 A101310 A101311
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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), Dec 22 2004
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