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

1,1

Comments

Shifts left and divides by 3 under Euler transform.

Links

Table of n, a(n) for n=1..22.

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

Formula

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

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 *)

Crossrefs

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

Sequence in context: A138315 A337849 A328267 * A369388 A174318 A338575

Adjacent sequences: A038056 A038057 A038058 * A038060 A038061 A038062

Keyword

nonn,eigen

Author

Christian G. Bower, Jan 04 1999

Status

approved