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A036374 Number of ternary rooted trees with n nodes and height at most 6. 3

%I #23 Oct 29 2020 03:26:38

%S 1,1,1,2,4,8,17,38,82,177,376,789,1638,3376,6894,13987,28181,56424,

%T 112282,222171,437098,855311,1664755,3223402,6209505,11901967,

%U 22700056,43083657,81376732,152971812,286199220,532954482,987861697,1822655134

%N Number of ternary rooted trees with n nodes and height at most 6.

%H Sean A. Irvine, <a href="/A036374/b036374.txt">Table of n, a(n) for n = 0..364</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]]; A036374 = T[6] (* _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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Last modified March 29 08:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)