User blog:Wythagoras/Extension to Friedmann's stuff

n(k) function
Definition of n(k): the maxium length of a sequence in 1 dimension, k symbols, where a block leaps from i to 2i

Definition of n(a,b,c): the maxium length of a sequence in b dimensions, a symbols, where a block leaps from i to ci

Bounds and values
n(1,b,c) = (2c-1)^b

n(2,1,c) = c^3+2c-1

n(a,b,c) > n(a^b^c) for a,b and c ≥ 2

TREE sequence
this extension combines the powers of tree and TREE:

TREE(a,b) = a different brackets with a maxium of n+b brackets.

Bounds and values
TREE(1,b) = tree(b)

TREE(a,0) = TREE(a)

SCG
this extension is similiar to tree and TREE: you are allowed to use different colors of dots. The number of colors is b in the following definition: SCG(a,b).

I define F(a) as SCG(SCG(a),SCG(a))

Even F(0) = SCG(6,6) >>> SCG(13) is very very huge!