A120532 - OEIS

%I #4 Aug 21 2013 12:17:29

%S 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,

%T 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,

%U 1,1,0,0,1,1,1

%N First differences of successive generalized meta-Fibonacci numbers A120510.

%H 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]

%H 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>

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

%F 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.

%F 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.

%p d := n -> if n=1 then 1 else A120510(n)-A120510(n-1) fi;

%Y Cf. A120510, A120521.

%K nonn

%O 1,1

%A _Frank Ruskey_ and Chris Deugau (deugaucj(AT)uvic.ca), Jun 20 2006