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 A036375 Number of ternary rooted trees with n nodes and height at most 7. 3
 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 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

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Last modified December 9 11:11 EST 2023. Contains 367690 sequences. (Running on oeis4.)