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A052757
Number of rooted identity trees with n nodes and 3-colored non-root nodes.
8
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
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
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
New name from Vaclav Kotesovec, Feb 24 2015
STATUS
approved