%I
%S 1,1,1,2,3,4,4,5,4,4,3,2,1,1
%N Number of ternary rooted trees with n nodes and height at most 3.
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F If T_i(z) = g.f. for ternary trees of height at most i, T_{i+1}(z)=1+z*(T_i(z)^3/6+T_i(z^2)*T_i(z)/2+T_i(z^3)/3); T_0(z) = 1.
%t T[0] = {1}; T[n_] := T[n] = Module[{f, g}, f[z_] := Sum[T[n  1][[i]]*z^(i  1), {i, 1, Length[T[n  1]]}]; g = 1 + z*(f[z]^3/6 + f[z^2]*f[z]/2 + f[z^3]/3); CoefficientList[g, z]]; A036371 = T[3] (* _JeanFrançois Alcover_, Jan 19 2016, after _Alois P. Heinz_ (A036370) *)
%Y Cf. A036370.
%K nonn,full,fini
%O 0,4
%A _N. J. A. Sloane_, E. M. Rains (rains(AT)caltech.edu)
