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A126189
Number of hex trees with n edges and no adjacent vertices of outdegree 2.
1
1, 3, 10, 36, 135, 519, 2034, 8100, 32688, 133380, 549342, 2280690, 9534591, 40103019, 169583382, 720549432, 3074694552, 13170845916, 56616211818, 244144402182, 1055875341888, 4578616787256, 19903066450722, 86713862341590
OFFSET
0,2
COMMENTS
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).
LINKS
F. Harary and R. C. Read, The enumeration of tree-like polyhexes, Proc. Edinburgh Math. Soc. (2) 17 (1970), 1-13.
FORMULA
a(n) = A126188(n,0).
G.f.: [1-3z-6z^3-sqrt(1-6z+9z^2-12z^3)]/(18z^4).
D-finite with recurrence (n+4)*a(n) +3*(-2*n-5)*a(n-1) +9*(n+1)*a(n-2) +6*(-2*n+1)*a(n-3)=0. - R. J. Mathar, Jun 17 2016
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);
MATHEMATICA
CoefficientList[Series[(1-3x-6x^3-Sqrt[1-6x+9x^2-12x^3])/(18x^4), {x, 0, 30}], x] (* Harvey P. Dale, Oct 25 2011 *)
CROSSREFS
Cf. A126188.
Sequence in context: A126188 A081909 A371873 * A122448 A007582 A369436
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Dec 25 2006
STATUS
approved