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A240835 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=4.

%I A240835 #23 Dec 06 2023 14:08:00
%S A240835 1,1,1,1,4,4,4,4,7,7,7,10,7,10,13,10,13,13,13,16,16,16,16,16,19,19,19,
%T A240835 22,19,22,25,22,25,25,25,28,28,28,28,31,31,31,34,31,34,37,34,37,37,34,
%U A240835 40,40,37,43,40,40,46,43,43,46,46,46,49,49,46,52,52,49,55,52,52,58,55,55,58,55,58,61,58,61,61,61
%N A240835 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=4.
%H A240835 N. J. A. Sloane, <a href="/A240835/b240835.txt">Table of n, a(n) for n = 1..20000</a>
%H A240835 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) and Table 6.1
%H A240835 <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>
%p A240835 #T_s,k(n) from Callaghan et al. Eq. (1.7).
%p A240835 s:=0; k:=4;
%p A240835 a:=proc(n) option remember; global s,k;
%p A240835 if n <= s+k then 1
%p A240835 else
%p A240835     add(a(n-i-s-a(n-i-1)),i=0..k-1);
%p A240835 fi; end;
%p A240835 t1:=[seq(a(n),n=1..100)];
%t A240835 A240835[n_]:=A240835[n]=If[n<=4,1,Sum[A240835[n-i-A240835[n-i-1]],{i,0,3}]];
%t A240835 Array[A240835,100] (* _Paolo Xausa_, Dec 06 2023 *)
%Y A240835 Callaghan et al. (2005)'s sequences T_{0,k}(n) for k=1 through 7 are A000012, A046699, A046702, A240835, A241154, A241155, A240830.
%K A240835 nonn,hear
%O A240835 1,5
%A A240835 _N. J. A. Sloane_, Apr 16 2014