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%I #9 Mar 16 2021 05:28:43
%S 1,1,1,1,2,3,4,4,4,4,4,5,6,7,8,8,9,10,11,12,12,13,14,15,16,16,16,16,
%T 16,16,17,18,19,20,20,21,22,23,24,24,25,26,27,28,28,29,30,31,32,32,32,
%U 33,34,35,36,36,37,38,39,40
%N Generalized meta-Fibonacci sequence a(n) with parameters s=3 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 If 1 <= n <= 4, a(n)=1. If 5 <= n <= 7, then a(n)=n-3. If n>7 then a(n)=a(n-3-a(n-1)) + a(n-4-a(n-2)) + a(n-5-a(n-3)) + a(n-6-a(n-4)).
%F G.f.: A(z) = z * (1 - z^3) / (1 - z) * sum(prod(z^3 * (1 - z^(4 * [i])) / (1 - z^[i]), i=1..n), n=0..infinity), where [i] = (4^i - 1) / 3.
%p a := proc(n)
%p option remember;
%p if n <= 4 then return 1 end if;
%p if n <= 7 then return n-3 end if;
%p return add(a(n - i - 2 - a(n - i)), i = 1 .. 4)
%p end proc
%Y Cf. A120521, A120532.
%K nonn
%O 1,5
%A _Frank Ruskey_ and Chris Deugau (deugaucj(AT)uvic.ca), Jun 20 2006
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