A036371 Number of ternary rooted trees with n nodes and height at most 3.

1, 1, 1, 2, 3, 4, 4, 5, 4, 4, 3, 2, 1, 1

Offset: 0

Author

N. J. A. Sloane, E. M. Rains (rains(AT)caltech.edu)

Keywords

• nonn
• full
• fini

Links

• Index entries for sequences related to rooted trees

Crossrefs

Cf. A036370.

Programs

Mathematica

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] (* Jean-François Alcover, Jan 19 2016, after Alois P. Heinz (A036370) *)

Formula

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.