A052757 Number of rooted identity trees with n nodes and 3-colored non-root nodes.

0, 1, 3, 12, 64, 363, 2214, 14043, 91857, 614676, 4189254, 28974915, 202870938, 1435094800, 10241197917, 73639001172, 533004547453, 3880381334415, 28395656513145, 208748382089131, 1540935621796941, 11417266889312313, 84880193073070819, 632976019285857201

Offset

0,3

Comments

Previous name was: A simple grammar.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 713

Formula

a(n) ~ c * d^n / n^(3/2), where d = 7.969494030514425004826375511986491746399264355846412073489715938424..., c = 0.12982932099206082951153936270704832022771078... . - Vaclav Kotesovec, Feb 24 2015

From Ilya Gutkovskiy, Apr 13 2019: (Start)

G.f. A(x) satisfies: A(x) = x*exp(3*Sum_{k>=1} (-1)^(k+1)*A(x^k)/k).

G.f.: A(x) = Sum_{n>=1} a(n)*x^n = x * Product_{n>=1} (1 + x^n)^(3*a(n)). (End)

Example

a(3) = 12:
o  o  o  o  o  o  o  o  o    o      o      o
|  |  |  |  |  |  |  |  |   / \    / \    / \
1  1  1  2  2  2  3  3  3  1   2  1   3  2   3
|  |  |  |  |  |  |  |  |
1  2  3  1  2  3  1  2  3  - Alois P. Heinz, Feb 24 2015

Maple

spec := [S, {S=Prod(B, B, B, Z), B=PowerSet(S)}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);

Crossrefs

Cf. A038079.

Column k=3 of A255517.

Sequence in context: A172450 A276743 A203508 * A345883 A365122 A233397

Adjacent sequences: A052754 A052755 A052756 * A052758 A052759 A052760

Keyword

easy,nonn

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Extensions

New name from Vaclav Kotesovec, Feb 24 2015

Status

approved