cp's OEIS Frontend

A126184 Number of hex trees with n edges and having no nonroot nodes of outdegree 2.

%I A126184 #27 Jun 29 2023 19:14:17
%S A126184 1,3,10,33,108,351,1134,3645,11664,37179,118098,373977,1180980,
%T A126184 3720087,11691702,36669429,114791256,358722675,1119214746,3486784401,
%U A126184 10847773692,33705582543,104603532030,324270949293,1004193907488
%N A126184 Number of hex trees with n edges and having no nonroot nodes of outdegree 2.
%C A126184 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 A126184 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.
%H A126184 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6, -9).
%F A126184 a(n) = A126183(n,0).
%F A126184 a(n) = (n+8)*3^(n-2) for n >= 1; a(0)=1.
%F A126184 G.f.: (1-3z+z^2)/(1-3z)^2.
%F A126184 From _Paul Curtz_, Mar 27 2022: (Start)
%F A126184 a(n+1) = 3*a(n) + A140429(n), for n >= 0; a(0)=1.
%F A126184 Binomial transform of A172481(n) for n >= 0.
%F A126184 Also, with a different offset, the binomial transform of A045891(n+2) for n >= 0. (End)
%p A126184 1,seq(3^(n-2)*(n+8),n=1..28);
%Y A126184 Cf. A126183.
%Y A126184 Cf. A045891, A140429, A172481.
%K A126184 nonn
%O A126184 0,2
%A A126184 _Emeric Deutsch_, Dec 19 2006