A126189 Number of hex trees with n edges and no adjacent vertices of outdegree 2.

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

Author

Emeric Deutsch, Dec 25 2006

Keywords

• nonn

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.

Crossrefs

Cf. A126188.

Programs

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 *)

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