A036376 Number of ternary rooted trees with n nodes and height at most 8.

1, 1, 1, 2, 4, 8, 17, 39, 89, 210, 498, 1185, 2813, 6664, 15707, 36886, 86259, 201003, 466788, 1080825, 2495565, 5747664, 13206253, 30276788, 69267205, 158155198, 360422113, 819873747, 1861732042, 4220347570, 9551287776

Offset

0,4

Links

Sean A. Irvine, Table of n, a(n) for n = 0..3280

E. M. Rains and N. J. A. Sloane, On Cayley's Enumeration of Alkanes (or 4-Valent Trees), J. Integer Sequences, Vol. 2 (1999), Article 99.1.1.

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]]; A036376 = T[8][[1 ;; 40]] (* Jean-François Alcover, Jan 19 2016, after Alois P. Heinz (A036370) *)

Crossrefs

Cf. A036370.

Sequence in context: A241671 A368095 A036375 * A000598 A003008 A185352

Adjacent sequences: A036373 A036374 A036375 * A036377 A036378 A036379

Keyword

nonn,fini,full

Author

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

Status

approved