editing

approved

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

approved

editing

C. Deugau and F. Ruskey, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL12/Ruskey/ruskey6.pdf">Complete k-ary Trees and Generalized Meta-Fibonacci Sequences</a>, J. Integer Seq., Vol. 12. [This is a later version than that in the GenMetaFib.html link]

nonn,new

nonn

First differences of successive generalized meta-Fibonacci numbers A120510.

1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1

1,1

C. Deugau and F. Ruskey, <a href="http://www.cs.uvic.ca/~ruskey/Publications/MetaFib/GenMetaFib.html">Complete k-ary Trees and Generalized Meta-Fibonacci Sequences</a>

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

g.f.: z (1 + z^4 ( (1 - z^(3 * [1])) / (1 - z^[1]) + z^7 * (1 - z^(4 * [i]))/(1 - z^[1]) ( (1 - z^(3 * [2])) / (1 - z^[2]) + z^19 * (1 - z^(4 * [2]))/(1 - z^[2]) (..., where [i] = (4^i - 1) / 3.

g.f.: D(z) = z * (1 - z^3) * sum(prod(z^3 * (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 A120510(n)-A120510(n-1) fi;

Cf. A120510, A120521.

nonn

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

approved