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A241155 a(n)=1 for n <= s+k; thereafter a(n) = Sum_{i=0..k-1} a(n-i-s-a(n-i-1)) where s=0, k=6.

%I A241155 #16 Dec 06 2023 11:24:07
%S A241155 1,1,1,1,1,1,6,6,6,6,6,6,11,11,11,11,11,16,11,16,16,16,21,16,21,16,21,
%T A241155 26,21,26,21,26,26,26,31,26,31,31,31,31,31,36,36,36,36,36,36,36,41,41,
%U A241155 41,41,41,46,41,46,46,46,51,46,51,46,51,56,51,56,51,56,56,56,61,56,61,61,61,61,61,66,66,66,66,66
%N A241155 a(n)=1 for n <= s+k; thereafter a(n) = Sum_{i=0..k-1} a(n-i-s-a(n-i-1)) where s=0, k=6.
%H A241155 N. J. A. Sloane, <a href="/A241155/b241155.txt">Table of n, a(n) for n = 1..20000</a>
%H A241155 Joseph Callaghan, John J. Chew III, and Stephen M. Tanny, <a href="https://doi.org/10.1137/S0895480103421397">On the behavior of a family of meta-Fibonacci sequences</a>, SIAM Journal on Discrete Mathematics 18.4 (2005): 794-824. See Eq. (1.7).
%H A241155 <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>
%p A241155 #T_s,k(n) from Callaghan et al. Eq. (1.7).
%p A241155 s:=0; k:=6;
%p A241155 a:=proc(n) option remember; global s,k;
%p A241155 if n <= s+k then 1
%p A241155 else
%p A241155 add(a(n-i-s-a(n-i-1)),i=0..k-1);
%p A241155 fi; end;
%p A241155 t1:=[seq(a(n),n=1..100)];
%t A241155 A241155[n_]:=A241155[n]=If[n<=6,1,Sum[A241155[n-i-A241155[n-i-1]],{i,0,5}]];
%t A241155 Array[A241155,100] (* _Paolo Xausa_, Dec 06 2023 *)
%Y A241155 Callaghan et al. (2005)'s sequences T_{0,k}(n) for k=1 through 7 are A000012, A046699, A046702, A240835, A241154, A241155, A240830.
%K A241155 nonn
%O A241155 1,7
%A A241155 _N. J. A. Sloane_, Apr 16 2014