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A178770 a(0) = a(1) = a(2) = a(3) = a(4) = 1, thereafter a(n) = a(a(n-1)) + a(n-a(n-3)).

%I A178770 #15 Jun 06 2018 03:32:24
%S A178770 1,1,1,1,1,2,3,4,4,4,4,5,6,7,8,8,8,8,8,9,10,11,12,13,14,15,15,15,15,
%T A178770 16,16,16,16,16,16,17,18,19,20,21,22,23,24,25,26,26,26,26,27,28,29,30,
%U A178770 30,30,30,31,31,31,31,31,32,32,32,32,32,32,32,33,34,35,36,37,38,39,40
%N A178770 a(0) = a(1) = a(2) = a(3) = a(4) = 1, thereafter a(n) = a(a(n-1)) + a(n-a(n-3)).
%C A178770 The sequence has many plateaus where numbers repeat three times or more. 16 appears 6 times in a row. The long start up vector produces this phase locking / staircase behavior which is probably due to feedback effects.
%H A178770 Muniru A Asiru, <a href="/A178770/b178770.txt">Table of n, a(n) for n = 0..10000</a>
%p A178770 a:= proc(n) option remember: if n<5 then 1 else procname(procname(n-1))+procname(n-procname(n-3)) fi end: seq(a(n), n=0..80); # _Muniru A Asiru_, Jun 05 2018
%t A178770 a[0] = 1; a[1] = 1; a[2] = 1; a[3] = 1;
%t A178770 a[4] = 1;(*a[4]=3;a[5]=2;a[6]=3*);
%t A178770 a[n_Integer] := a[n] = a[a[n - 1]] + a[n - a[-3 + n]]
%t A178770 b = Table[a[n], {n, 0, 200}]
%o A178770 (GAP) a:=[1,1,1,1];; for n in [5..80] do a[n]:=a[a[n-1]]+a[n-a[n-3]]; od;
%o A178770 a:=Concatenation([1],a); # _Muniru A Asiru_, Jun 05 2018
%Y A178770 Cf. A004001.
%K A178770 nonn,easy
%O A178770 0,6
%A A178770 _Roger L. Bagula_, Jun 11 2010