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 A120523 First differences of successive meta-Fibonacci numbers A120501. 2

%I

%S 1,0,0,1,0,0,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0,0,0,1,1,0,1,1,0,0,1,1,0,1,

%T 1,0,0,0,0,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,1,1,

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

%N First differences of successive meta-Fibonacci numbers A120501.

%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>

%H B. Jackson and F. Ruskey, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v13i1r26">Meta-Fibonacci Sequences, Binary Trees and Extremal Compact Codes</a>, Electronic Journal of Combinatorics, 13 (2006), #R26, 13 pages.

%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^3 ( (1 - z^[1]) / (1 - z^[1]) + z^4 * (1 - z^(2 * [i]))/(1 - z^[1]) ( (1 - z^[2]) / (1 - z^[2]) + z^6 * (1 - z^(2 * [2]))/(1 - z^[2]) (..., where [i] = (2^i - 1).

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

%p d := n -> if n=1 then 1 else A120501(n)-A120501(n-1) fi;

%Y Cf. A120501, A120512.

%K nonn

%O 1,1

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

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Last modified January 17 23:37 EST 2020. Contains 330995 sequences. (Running on oeis4.)