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%I #23 Oct 29 2020 03:26:18
%S 1,1,1,2,4,8,17,39,88,203,464,1056,2381,5344,11900,26381,58165,127713,
%T 279209,608213,1319985,2855275,6155981,13231553,28353787,60583959,
%U 129084369,274283708,581244959,1228514486,2589902750,5446168197
%N Number of ternary rooted trees with n nodes and height at most 7.
%H Sean A. Irvine, <a href="/A036375/b036375.txt">Table of n, a(n) for n = 0..1093</a>
%H E. M. Rains and N. J. A. Sloane, <a href="https://cs.uwaterloo.ca/journals/JIS/cayley.html">On Cayley's Enumeration of Alkanes (or 4-Valent Trees)</a>, J. Integer Sequences, Vol. 2 (1999), Article 99.1.1.
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F 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.
%t 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) *)
%Y Cf. A036370.
%K nonn,fini,full
%O 0,4
%A _N. J. A. Sloane_, E. M. Rains (rains(AT)caltech.edu)
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