|
%I #16 Nov 01 2020 07:46:27
%S 1,3,6,18,75,342,1773,9894,58596,362061,2314119,15185223,101830986,
%T 695253993,4819762446,33851833506,240472935735,1725315714729,
%U 12487872432924,91097741283408,669227023979088,4947500029023540,36786363204267282,274949933519917908
%N Number of trees with 3-colored nodes.
%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F G.f.: B(x) - B^2(x)/2 + B(x^2)/2, where B(x) is g.f. for A038059.
%t b[n_] := b[n] = If[n < 2, 3n, (Sum[Sum[b[d] d, {d, Divisors[j]}] b[n - j], {j, 1, n - 1}])/(n - 1)];
%t a[n_] := If[n == 0, 1, b[n] - (Sum[b[k] b[n - k], {k, 0, n}] - If[Mod[n, 2] == 0, b[n/2], 0])/2];
%t a /@ Range[0, 25] (* _Jean-François Alcover_, Nov 01 2020, after _Alois P. Heinz_ in A006965 *)
%Y Cf. A000055, A038055-A038062.
%Y Equals 3 * A006965(n).
%K nonn
%O 0,2
%A _Christian G. Bower_, Jan 04 1999
|
