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^1 ( (1 - z^(3 * [1])) / (1 - z^[1]) + z^4 * (1 - z^(4 * [i]))/(1 - z^[1]) ( (1 - z^(3 * [2])) / (1 - z^[2]) + z^16 * (1 - z^(4 * [2]))/(1 - z^[2]) (..., where [i] = (4^i - 1) / 3.

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

d := n -> if n=1 then 1 else A120507(n)-A120507(n-1) fi;

Cf. A120507, A120518.

Sequence in context: A051731 A135839 A155076 this_sequence A099443 A132342 A156174

Adjacent sequences: A120526 A120527 A120528 this_sequence A120530 A120531 A120532

nonn

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