OFFSET
0,3
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
G. C. Greubel, Table of n, a(n) for n = 0..1000
F. Harary and R. C. Read, The enumeration of tree-like polyhexes, Proc. Edinburgh Math. Soc. (2) 17 (1970), 1-13.
FORMULA
a(n) = A126321(n,0).
G.f.: (1-3z+9z^2)[1-3z-sqrt(1-6z+9z^2-36z^4)]/(18z^4).
Conjecture: (n+4)*(25*n^2+230*n+1137)*a(n) +3*(-50*n^3-585*n^2-3169*n-4248) *a(n-1) +9*(25*n^3+255*n^2+932*n-1764) *a(n-2) +29484*a(n-3) -36*(n-4) *(25*n^2+280*n+1392) *a(n-4)=0. - R. J. Mathar, Jun 17 2016
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);
MATHEMATICA
CoefficientList[Series[(1 - 3*x + 9*x^2)*(1 - 3*x - Sqrt[1 - 6*x + 9*x^2 - 36*x^4])/(18*x^4), {x, 0, 30}], x] (* G. C. Greubel, Oct 23 2018 *)
PROG
(PARI) x='x+O('x^30); Vec((1-3*x+9*x^2)*(1-3*x-sqrt(1-6*x+9*x^2-36*x^4) )/(18*x^4)) \\ G. C. Greubel, Oct 23 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R!((1 -3*x+9*x^2)*(1-3*x -Sqrt(1-6*x+9*x^2-36*x^4))/(18*x^4))); // G. C. Greubel, Oct 23 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Dec 25 2006
STATUS
approved