cp's OEIS Frontend

A126187 Sum of the levels of the first leaf (in the preorder traversal) over all hex trees with n edges.

%I A126187 #9 Jul 24 2022 10:39:55
%S A126187 3,19,96,453,2085,9513,43323,197542,903141,4142565,19067202,88065360,
%T A126187 408108285,1897265405,8846769300,41368049400,193950461985,
%U A126187 911564782065,4294230794520,20273068467725,95902496669091,454528832324919
%N A126187 Sum of the levels of the first leaf (in the preorder traversal) over all hex trees with n edges.
%C A126187 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 A126187 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 A126187 a(n) = Sum_{k=1..n} k*A126186(n,k).
%F A126187 G.f.: 2[1+3z-sqrt(1-6z+5z^2)]/[1-3z+sqrt(1-6z+5z^2)]^2.
%F A126187 D-finite with recurrence (n-1)*(3*n-1)*(n+4)*a(n) -n*(18*n^2+21*n-19)*a(n-1) +5*n*(3*n+2)*(n-1)*a(n-2)=0. - _R. J. Mathar_, Jun 17 2016
%p A126187 g:=2*(1+3*z-sqrt(1-6*z+5*z^2))/(1-3*z+sqrt(1-6*z+5*z^2))^2: gser:=series(g,z=0,28): seq(coeff(gser,z,n),n = 1..25);
%Y A126187 Cf. A126186.
%K A126187 nonn
%O A126187 1,1
%A A126187 _Emeric Deutsch_, Dec 22 2006