A038060 Number of trees with 3-colored nodes.

1, 3, 6, 18, 75, 342, 1773, 9894, 58596, 362061, 2314119, 15185223, 101830986, 695253993, 4819762446, 33851833506, 240472935735, 1725315714729, 12487872432924, 91097741283408, 669227023979088, 4947500029023540, 36786363204267282, 274949933519917908

Offset

0,2

Links

Table of n, a(n) for n=0..23.

Index entries for sequences related to trees

Formula

G.f.: B(x) - B^2(x)/2 + B(x^2)/2, where B(x) is g.f. for A038059.

Mathematica

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)];
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];
a /@ Range[0, 25] (* Jean-François Alcover, Nov 01 2020, after Alois P. Heinz in A006965 *)

Crossrefs

Cf. A000055, A038055-A038062.

Equals 3 * A006965(n).

Sequence in context: A102962 A076510 A220816 * A366607 A345134 A135504

Adjacent sequences: A038057 A038058 A038059 * A038061 A038062 A038063

Keyword

nonn

Author

Christian G. Bower, Jan 04 1999

Status

approved