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A241154 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=5.

%I A241154 #22 Nov 10 2017 05:13:43
%S A241154 1,1,1,1,1,5,5,5,5,5,9,9,9,9,13,9,13,13,17,13,17,13,17,17,21,17,21,21,
%T A241154 21,21,25,25,25,25,25,29,29,29,29,33,29,33,33,37,33,37,33,41,37,41,37,
%U A241154 45,37,45,41,49,41,49,41,53,45,53,45,57,45,57,49,61,49,61,49,61,53,65,53,65,57,65,57,69,61,69,61
%N A241154 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=5.
%H A241154 N. J. A. Sloane, <a href="/A241154/b241154.txt">Table of n, a(n) for n = 1..20000</a>
%H A241154 Joseph Callaghan, John J. Chew III, and Stephen M. Tanny, <a href="http://dx.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 A241154 <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>
%p A241154 #T_s,k(n) from Callaghan et al. Eq. (1.7).
%p A241154 s:=0; k:=5;
%p A241154 a:=proc(n) option remember; global s,k;
%p A241154 if n <= s+k then 1
%p A241154 else
%p A241154 add(a(n-i-s-a(n-i-1)),i=0..k-1);
%p A241154 fi; end;
%p A241154 t1:=[seq(a(n),n=1..100)];
%t A241154 s = 0; k = 5; a[n_] := a[n] = If[n <= s + k, 1, Sum[a[n - i - s - a[n - i - 1]], {i, 0, k - 1}]]; Array[a, 100] (* _Jean-François Alcover_, Nov 10 2017 *)
%Y A241154 Callaghan et al. (2005)'s sequences T_{0,k}(n) for k=1 through 7 are A000012, A046699, A046702, A240835, A241154, A241155, A240830.
%K A241154 nonn,hear,look
%O A241154 1,6
%A A241154 _N. J. A. Sloane_, Apr 16 2014