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

Author

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

Keywords

• easy
• nonn

Comments

Previous name was: A simple grammar.

Examples

			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
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 713

Crossrefs

Cf. A038079.

Column k=3 of A255517.

Programs

Maple

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

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)

Extensions

New name from Vaclav Kotesovec, Feb 24 2015