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^3 ( (1 - z^(2 * [1])) / (1 - z^[1]) + z^5 * (1 - z^(3 * [i]))/(1 - z^[1]) ( (1 - z^(2 * [2])) / (1 - z^[2]) + z^11 * (1 - z^(3 * [2]))/(1 - z^[2]) (..., where [i] = (3^i - 1) / 2.

g.f.: D(z) = z * (1 - z^2) * sum(prod(z^2 * (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 A120505(n)-A120505(n-1) fi;

Cf. A120505, A120516.

Sequence in context: A104105 A143221 A126999 this_sequence A071004 A102560 A068428

Adjacent sequences: A120524 A120525 A120526 this_sequence A120528 A120529 A120530

nonn

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