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 A036376 Number of ternary rooted trees with n nodes and height at most 8. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS 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 Cf. A036370. Sequence in context: A055545 A241671 A036375 * A000598 A003008 A185352 Adjacent sequences:  A036373 A036374 A036375 * A036377 A036378 A036379 KEYWORD nonn,fini AUTHOR N. J. A. Sloane, E. M. Rains (rains(AT)caltech.edu) STATUS approved

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Last modified June 16 13:37 EDT 2019. Contains 324152 sequences. (Running on oeis4.)