A036375 Number of ternary rooted trees with n nodes and height at most 7.

1, 1, 1, 2, 4, 8, 17, 39, 88, 203, 464, 1056, 2381, 5344, 11900, 26381, 58165, 127713, 279209, 608213, 1319985, 2855275, 6155981, 13231553, 28353787, 60583959, 129084369, 274283708, 581244959, 1228514486, 2589902750, 5446168197

Offset

0,4

Links

Sean A. Irvine, Table of n, a(n) for n = 0..1093

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]]; A036375 = T[7] (* Jean-François Alcover, Jan 19 2016, after Alois P. Heinz (A036370) *)

Crossrefs

Cf. A036370.

Sequence in context: A132043 A055545 A241671 * A036376 A000598 A003008

Adjacent sequences: A036372 A036373 A036374 * A036376 A036377 A036378

Keyword

nonn,fini,full

Author

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

Status

approved