OFFSET
1,1
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
EXAMPLE
Triangle starts:
3;
1, 9;
3, 6, 27;
10, 19, 27, 81;
36, 66, 90, 108, 243;
MAPLE
G:=2/(2-t-3*t*z+t*sqrt(1-6*z+5*z^2))-1: Gser:=simplify(series(G, z=0, 14)): for n from 1 to 10 do P[n]:=sort(coeff(Gser, z, n)) od: for n from 1 to 10 do seq(coeff(P[n], t, k), k=1..n) od; # yields sequence in triangular form
MATHEMATICA
n = 10; g[t_, z_] = 2/(2 - t - 3t*z + t*Sqrt[1 - 6z + 5z^2]) - 1; Flatten[ Rest[ CoefficientList[#, t]] & /@ Rest[ CoefficientList[ Series[g[t, z], {z, 0, n}], z]]] (* Jean-François Alcover, Jul 22 2011, after g.f. *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Emeric Deutsch, Dec 22 2006
STATUS
approved