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A036372 Number of ternary rooted trees with n nodes and height at most 4. 2
1, 1, 1, 2, 4, 7, 12, 20, 31, 47, 70, 99, 137, 184, 239, 300, 369, 432, 498, 551, 594, 614, 624, 601, 570, 514, 453, 378, 312, 238, 181, 128, 89, 56, 37, 20, 12, 6, 3, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..40.

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]]; A036372 = T[4] (*Jean-Fran├žois Alcover, Jan 19 2016, after Alois P. Heinz (A036370) *)

CROSSREFS

Cf. A036370.

Sequence in context: A010672 A122515 A193840 * A132218 A101230 A128129

Adjacent sequences:  A036369 A036370 A036371 * A036373 A036374 A036375

KEYWORD

nonn,full,fini

AUTHOR

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

STATUS

approved

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Last modified August 4 21:32 EDT 2021. Contains 346455 sequences. (Running on oeis4.)