

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
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OFFSET

0,4


LINKS



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] (* JeanFrançois Alcover, Jan 19 2016, after Alois P. Heinz (A036370) *)


CROSSREFS



KEYWORD

nonn,fini,full


AUTHOR



STATUS

approved



