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Search: id:A126323
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| A126323 |
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Number of branches of length 1 in all hex trees with n edges. A hex tree is a rooted tree where each vertex has 0, 1, or 2 children and, when only one child is present, it is either a left child, or a middle child, or a right child (name due to an obvious bijection with certain tree-like polyhexes; see the Harary-Read reference). |
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+0
2
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| 0, 3, 2, 15, 80, 399, 1956, 9546, 46552, 227100, 1108698, 5417127, 26490312, 129645027, 634978290, 3112277265, 15264984260, 74919716085, 367926876630, 1807912844925, 8888531467360, 43722603214365, 215175747222640
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n)=Sum(k*A126321(n,k),k=0..n).
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REFERENCES
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F. Harary and R. C. Read, The enumeration of tree-like polyhexes, Proc. Edinburgh Math. Soc. (2) 17 (1970), 1-13.
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FORMULA
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G.f.=(1-3z)^2*[2-9z+5z^2-(2-3z)sqrt(1-6z+5z^2)]/[2z^2*sqrt(1-6z+5z^2)].
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MAPLE
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g:=(1-3*z)^2*(2-9*z+5*z^2-(2-3*z)*sqrt(1-6*z+5*z^2))/2/z^2/sqrt(1-6*z+5*z^2): gser:=series(g, z=0, 33): seq(coeff(gser, z, n), n=0..27);
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CROSSREFS
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Cf. A126321.
Sequence in context: A051917 A133932 A111999 this_sequence A084886 A055864 A072045
Adjacent sequences: A126320 A126321 A126322 this_sequence A126324 A126325 A126326
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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 25 2006
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