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A126322
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Number of hex trees with n edges and no branches of length 1. 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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1
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1, 0, 9, 27, 90, 297, 1053, 3888, 14742, 56619, 219429, 857304, 3375999, 13391001, 53452467, 214525017, 865041606, 3502806363, 14237599635, 58069495188, 237583710549, 974819569095, 4010205424869, 16536842688267, 68344258564980
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n)=A126321(n,0).
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REFERENCES
| 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
| G.f.=(1-3z+9z^2)[1-3z-sqrt(1-6z+9z^2-36z^4)]/(18z^4).
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MAPLE
| g:=(1-3*z+9*z^2)*(1-3*z-sqrt((1-3*z)^2-36*z^4))/18/z^4: gser:=series(g, z=0, 32): seq(coeff(gser, z, n), n=0..27);
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CROSSREFS
| Cf. A126321.
Sequence in context: A036314 A036317 A053762 * A020279 A057901 A020254
Adjacent sequences: A126319 A126320 A126321 * A126323 A126324 A126325
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 25 2006
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