cp's OEIS Frontend

A126190 Number of pairs of adjacent vertices of outdegree 2 in all hex trees with n edges.

%I A126190 #7 Dec 29 2016 15:38:52
%S A126190 0,0,0,0,2,24,190,1260,7602,43344,238308,1278360,6739590,35086392,
%T A126190 180952200,926583840,4718481950,23923888800,120881319280,609086170080,
%U A126190 3062089990710,15365797583400,76989505040350,385265732393388
%N A126190 Number of pairs of adjacent vertices of outdegree 2 in all hex trees with n edges.
%C A126190 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 A126190 Robert Israel, <a href="/A126190/b126190.txt">Table of n, a(n) for n = 0..1432</a>
%H A126190 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 A126190 a(n) = Sum_{k=0..floor(n/2)-1} k*A126188(n,k).
%F A126190 G.f.: [1-9z+24z^2-18z^3-(1-6z+8z^2)sqrt(1-6z+5z^2)]/[z^2*sqrt(1-6z+5z^2)].
%F A126190 90*n*a(n)+(-294-228*n)*a(n+1)+(558+207*n)*a(2+n)+(-345-83*n)*a(n+3)+(84+15*n)*a(n+4)+(-7-n)*a(n+5) = 0. - _Robert Israel_, Dec 29 2016
%p A126190 G:=(1-9*z+24*z^2-18*z^3-(1-6*z+8*z^2)*sqrt(1-6*z+5*z^2))/z^2/sqrt(1-6*z+5*z^2): Gser:=series(G,z=0,32): seq(coeff(Gser,z,n),n=0..27);
%Y A126190 Cf. A126188.
%K A126190 nonn
%O A126190 0,5
%A A126190 _Emeric Deutsch_, Dec 25 2006