1,1

C. Deugau and F. Ruskey, Complete k-ary Trees and Generalized Meta-Fibonacci Sequences, J. Integer Seq., Vol. 12. [This is a later version than that in the GenMetaFib.html link]

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^(2 * [1])) / (1 - z^[1]) + z^4 * (1 - z^(3 * [i]))/(1 - z^[1]) ( (1 - z^(2 * [2])) / (1 - z^[2]) + z^10 * (1 - z^(3 * [2]))/(1 - z^[2]) (..., where [i] = (3^i - 1) / 2.

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

d := n -> if n=1 then 1 else A120504(n)-A120504(n-1) fi;

Cf. A120504, A120515.

Sequence in context: A108882 A070829 A118175 this_sequence A086694 A093317 A127253

Adjacent sequences: A120523 A120524 A120525 this_sequence A120527 A120528 A120529

nonn

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