1,1

C. Deugau and F. Ruskey, Complete k-ary Trees and Generalized Meta-Fibonacci Sequences

d(n) = 0 if node n is an inner node, or 1 if node n is a leaf.

g.f.: z (1 + z^2 ( (1 - z^(3 * [1])) / (1 - z^[1]) + z^5 * (1 - z^(4 * [i]))/(1 - z^[1]) ( (1 - z^(3 * [2])) / (1 - z^[2]) + z^17 * (1 - z^(4 * [2]))/(1 - z^[2]) (..., where [i] = (4^i - 1) / 3.

g.f.: D(z) = z * (1-z) * sum(prod(z * (1 - z^(4 * [i])) / (1 - z^[i]), i=1..n), n=0..infinity), where [i] = (4^i - 1) / 3., Jun 20 2006

d := n -> if n=1 then 1 else A120508(n)-A120508(n-1) fi;

Cf. A120508, A120519.

Sequence in context: A118251 A099076 A030308 this_sequence A078616 A104106 A141260

Adjacent sequences: A120527 A120528 A120529 this_sequence A120531 A120532 A120533

nonn

Frank Ruskey (http://www.cs.uvic.ca/~ruskey/) and Chris Deugau (deugaucj(AT)uvic.ca), Jun 20 2006