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.
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
KEYWORD
nonn,fini,full
AUTHOR
N. J. A. Sloane, E. M. Rains (rains(AT)caltech.edu)
STATUS
approved