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A036375 Number of ternary rooted trees with n nodes and height at most 7. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..31.

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-Fran├žois 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

AUTHOR

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

STATUS

approved

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Last modified June 16 15:38 EDT 2019. Contains 324153 sequences. (Running on oeis4.)