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A120509 Generalized Meta-fibonacci sequence a(n) with parameters s=2 and k=4. 2

%I

%S 1,1,1,2,3,4,4,4,4,5,6,7,8,8,9,10,11,12,12,13,14,15,16,16,16,16,16,17,

%T 18,19,20,20,21,22,23,24,24,25,26,27,28,28,29,30,31,32,32,32,33,34,35,

%U 36,36,37,38,39,40,40,41,42

%N Generalized Meta-fibonacci sequence a(n) with parameters s=2 and k=4.

%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 g.f.: A(z) = z * (1 - z^2) / (1 - z) * sum(prod(z^2 * (1 - z^(4 * [i])) / (1 - z^[i]), i=1..n), n=0..infinity), where [i] = (4^i - 1) / 3.

%F If 1 <= n <= 3, a(n)=1. If 4 <= n <= 6, then a(n)=n-2. If n>6 then a(n)=a(n-2-a(n-1)) + a(n-3-a(n-2)) + a(n-4-a(n-3)) + a(n-5-a(n-4))

%p a := proc(n)

%p option remember;

%p if n <= 3 then return 1 end if;

%p if n <= 6 then return n-2 end if;

%p return add(a(n - i - 1 - a(n - i)), i = 1 .. 4)

%p end proc

%Y Cf. A120520, A120531.

%K nonn

%O 1,4

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

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Last modified April 8 03:01 EDT 2020. Contains 333312 sequences. (Running on oeis4.)