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^3 ( (1 - z^(3 * [1])) / (1 - z^[1]) + z^6 * (1 - z^(4 * [i]))/(1 - z^[1]) ( (1 - z^(3 * [2])) / (1 - z^[2]) + z^18 * (1 - z^(4 * [2]))/(1 - z^[2]) (..., where [i] = (4^i - 1) / 3.

g.f.: D(z) = z * (1 - z^2) * sum(prod(z^2 * (1 - z^(4 * [i])) / (1 - z^[i]), i=1..n), n=0..infinity), where [i] = (4^i - 1) / 3.

d := n -> if n=1 then 1 else A120509(n)-A120509(n-1) fi;

Cf. A120509, A120520.

Sequence in context: A083035 A051341 A057211 this_sequence A106665 A004609 A071001

Adjacent sequences: A120528 A120529 A120530 this_sequence A120532 A120533 A120534

nonn

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