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

0,4

Links

Table of n, a(n) for n=0..40.

Index entries for sequences related to rooted trees

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.

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) *)

Crossrefs

Cf. A036370.

Sequence in context: A010672 A122515 A193840 * A132218 A101230 A128129

Adjacent sequences: A036369 A036370 A036371 * A036373 A036374 A036375

Keyword

nonn,full,fini

Author

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

Status

approved