A036372 Number of ternary rooted trees with n nodes and height at most 4.

1, 1, 1, 2, 4, 7, 12, 20, 31, 47, 70, 99, 137, 184, 239, 300, 369, 432, 498, 551, 594, 614, 624, 601, 570, 514, 453, 378, 312, 238, 181, 128, 89, 56, 37, 20, 12, 6, 3, 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]]; A036372 = T[4] (*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.