cp's OEIS Frontend

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

%I A126189 #12 Jul 24 2022 10:40:49
%S A126189 1,3,10,36,135,519,2034,8100,32688,133380,549342,2280690,9534591,
%T A126189 40103019,169583382,720549432,3074694552,13170845916,56616211818,
%U A126189 244144402182,1055875341888,4578616787256,19903066450722,86713862341590
%N A126189 Number of hex trees with n edges and no adjacent vertices of outdegree 2.
%C A126189 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).
%H A126189 F. Harary and R. C. Read, <a href="https://doi.org/10.1017/S0013091500009135">The enumeration of tree-like polyhexes</a>, Proc. Edinburgh Math. Soc. (2) 17 (1970), 1-13.
%F A126189 a(n) = A126188(n,0).
%F A126189 G.f.: [1-3z-6z^3-sqrt(1-6z+9z^2-12z^3)]/(18z^4).
%F A126189 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
%p A126189 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);
%t A126189 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 *)
%Y A126189 Cf. A126188.
%K A126189 nonn
%O A126189 0,2
%A A126189 _Emeric Deutsch_, Dec 25 2006