A038059 Number of rooted trees with 3-colored nodes.

3, 9, 45, 246, 1485, 9432, 62625, 428319, 3000393, 21410436, 155106693, 1137703869, 8432624850, 63060142671, 475196487363, 3604851603690, 27507181503069, 210988219961637, 1625848092941463, 12580709718788622, 97714211996345868, 761528782558088202

Offset: 1

Author

Christian G. Bower, Jan 04 1999

Keywords

• nonn
• eigen

Comments

Shifts left and divides by 3 under Euler transform.

Links

• L. Foissy, Algebraic structures on typed decorated rooted trees, arXiv:1811.07572 [math.RA] (2018).
• R. J. Mathar, Topologically distinct sets of non-intersecting circles in the plane, arXiv:1603.00077 [math.CO] (2016), Table 4.
• N. J. A. Sloane, Transforms
• Index entries for sequences related to rooted trees
• Index entries for sequences related to trees

Crossrefs

Cf. A000081, A038055-A038062, A271879 (multisets).

Programs

Maple

with(numtheory): a:= proc(n) option remember; `if`(n<2, 3*n, (add(add(d*a(d), d=divisors(j)) *a(n-j), j=1..n-1))/ (n-1)) end: seq(a(n), n=1..30); # Alois P. Heinz, Sep 06 2008

Mathematica

a[n_] := a[n] = If[n<2, 3*n, Sum[Sum[d*a[d], {d, Divisors[j]}] *a[n-j], {j, 1, n-1}]/(n-1)]; Array[a, 30] (* Jean-François Alcover, Feb 24 2016, after Alois P. Heinz *)

Formula

a(n) = 3 * A006964(n).