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A126189
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Number of hex trees with n edges and no adjacent vertices of outdegree 2. 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, 3, 10, 36, 135, 519, 2034, 8100, 32688, 133380, 549342, 2280690, 9534591, 40103019, 169583382, 720549432, 3074694552, 13170845916, 56616211818, 244144402182, 1055875341888, 4578616787256, 19903066450722, 86713862341590
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n)=A126188(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-6z^3-sqrt(1-6z+9z^2-12z^3)]/(18z^4).
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MAPLE
| g:=1/18/z^4*(1-3*z-6*z^3-sqrt(1+9*z^2-6*z-12*z^3)): gser:=series(g, z=0, 30): seq(coeff(gser, z, n), n=0..26);
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MATHEMATICA
| CoefficientList[Series[(1-3x-6x^3-Sqrt[1-6x+9x^2-12x^3])/(18x^4), {x, 0, 30}], x] (* From Harvey P. Dale, Oct 25 2011 *)
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CROSSREFS
| Cf. A126188.
Sequence in context: A119374 A126188 A081909 * A122448 A007582 A026854
Adjacent sequences: A126186 A126187 A126188 * A126190 A126191 A126192
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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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