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A240829 a(1)=-1, a(2)=0, a(3)=1; thereafter a(n) = Sum(a(n-i-s-a(n-i-1)),i=0..k-1) where s=0, k=3.

%I A240829 #13 Apr 16 2014 16:59:58
%S A240829 -1,0,1,3,2,4,4,7,4,7,7,9,8,9,11,10,10,13,15,13,13,13,18,15,18,18,18,
%T A240829 18,18,23,23,20,19,23,28,27,23,25,27,28,25,26,28,30,31,32,33,33,32,34,
%U A240829 33,38,36,39,34,36,36,39,39,39,39,44,46,46,43,46,46,44,44,49,49,49,46,51,48,51,51,54,54,54,54,54
%N A240829 a(1)=-1, a(2)=0, a(3)=1; thereafter a(n) = Sum(a(n-i-s-a(n-i-1)),i=0..k-1) where s=0, k=3.
%D A240829 Callaghan, Joseph, John J. Chew III, and Stephen M. Tanny. "On the behavior of a family of meta-Fibonacci sequences." SIAM Journal on Discrete Mathematics 18.4 (2005): 794-824. See Fig. 1.7.
%H A240829 N. J. A. Sloane, <a href="/A240829/b240829.txt">Table of n, a(n) for n = 1..20000</a>
%H A240829 <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>
%p A240829 #T_s,k(n) from Callaghan et al. Eq. (1.6).
%p A240829 s:=0; k:=3;
%p A240829 a:=proc(n) option remember; global s,k;
%p A240829 if n <= 3 then n-2
%p A240829 else
%p A240829     add(a(n-i-s-a(n-i-1)),i=0..k-1);
%p A240829 fi; end;
%p A240829 t1:=[seq(a(n),n=1..100)];
%Y A240829 Same recurrence as A240828, A120503 and A046702.
%K A240829 sign,hear
%O A240829 1,4
%A A240829 _N. J. A. Sloane_, Apr 16 2014