A036373 Number of ternary rooted trees with n nodes and height at most 5.

1, 1, 1, 2, 4, 8, 16, 33, 63, 121, 225, 415, 749, 1344, 2365, 4129, 7106, 12104, 20354, 33883, 55706, 90628, 145729, 231801, 364555, 567206, 872727, 1328545, 2000536, 2980554, 4393287, 6407683, 9246830, 13204526, 18657905, 26088244

Offset

0,4

Links

Sean A. Irvine, Table of n, a(n) for n = 0..121

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]]; A036373 = T[5] (* Jean-François Alcover, Jan 19 2016, after Alois P. Heinz (A036370) *)

Crossrefs

Cf. A036370.

Sequence in context: A137181 A272698 A355548 * A119610 A121485 A308808

Adjacent sequences: A036370 A036371 A036372 * A036374 A036375 A036376

Keyword

nonn,fini,full

Author

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

Status

approved