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A240830 a(n)=1 for n <= s+k; thereafter a(n) = Sum(a(n-i-s-a(n-i-1)),i=0..k-1) where s=0, k=7.

%I A240830 #31 Dec 06 2023 14:07:42
%S A240830 1,1,1,1,1,1,1,7,7,7,7,7,7,7,13,13,13,13,13,13,19,13,19,19,19,19,25,
%T A240830 19,25,19,25,25,31,25,31,25,31,25,31,31,37,31,37,31,37,37,37,37,43,37,
%U A240830 43,43,43,43,43,43,49,49,49,49,49,49,49,55,55,55,55,55,55,61,55,61,61,61,61,67,61,67,61,67,67,73
%N A240830 a(n)=1 for n <= s+k; thereafter a(n) = Sum(a(n-i-s-a(n-i-1)),i=0..k-1) where s=0, k=7.
%H A240830 N. J. A. Sloane, <a href="/A240830/b240830.txt">Table of n, a(n) for n = 1..20000</a>
%H A240830 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 Table 2.1.
%H A240830 <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>
%p A240830 #T_s,k(n) from Callaghan et al. Eq. (1.7).
%p A240830 s:=0; k:=7;
%p A240830 a:=proc(n) option remember; global s,k;
%p A240830 if n <= s+k then 1
%p A240830 else
%p A240830     add(a(n-i-s-a(n-i-1)),i=0..k-1);
%p A240830 fi; end;
%p A240830 t1:=[seq(a(n),n=1..100)];
%t A240830 A240830[n_]:=A240830[n]=If[n<=7,1,Sum[A240830[n-i-A240830[n-i-1]],{i,0,6}]];
%t A240830 Array[A240830,100] (* _Paolo Xausa_, Dec 06 2023 *)
%Y A240830 Same recurrence as A240828, A120503 and A046702.
%Y A240830 See also A240831, A240832.
%Y A240830 Callaghan et al. (2005)'s sequences T_{0,k}(n) for k=1 through 7 are A000012, A046699, A046702, A240835, A241154, A241155, A240830.
%K A240830 nonn,look,hear
%O A240830 1,8
%A A240830 _N. J. A. Sloane_, Apr 16 2014