|
%I #8 Nov 27 2018 09:33:51
%S 1,0,0,0,1,0,0,0,0,1,1,0,0,0,0,0,1,1,0,1,1,0,0,0,0,0,0,1,1,0,1,1,0,0,
%T 1,1,0,1,1,0,0,0,0,0,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,
%U 1,1,0,1,1,0,0
%N First differences of successive meta-Fibonacci numbers A120502.
%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^4 ( (1 - z^[1]) / (1 - z^[1]) + z^5 * (1 - z^(2 * [i]))/(1 - z^[1]) ( (1 - z^[2]) / (1 - z^[2]) + z^7 * (1 - z^(2 * [2]))/(1 - z^[2]) (..., where [i] = (2^i - 1).
%F G.f.: D(z) = z * (1 - z^3) * sum(prod(z^3 * (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 A120502(n)-A120502(n-1) fi;
%Y Cf. A120502, A120513.
%K nonn
%O 1,1
%A _Frank Ruskey_ and Chris Deugau (deugaucj(AT)uvic.ca), Jun 20 2006
|
