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A284523 a(1) = a(2) = 1, a(3) = 2; a(n) = a(a(n-1)-1) + a(n-a(n-3)-1) for n > 3.

%I A284523 #12 May 08 2017 12:31:04
%S A284523 1,1,2,2,3,3,3,3,4,5,5,5,5,5,6,8,8,8,8,8,8,8,8,9,11,13,13,13,11,13,13,
%T A284523 13,13,13,13,13,13,14,16,19,21,19,16,14,16,17,21,21,21,21,19,21,21,21,
%U A284523 21,21,21,21,21,22,24,27,32,29,26,24,21,29,27,34,34,27,27,29,34,34,34,29,27,29,32
%N A284523 a(1) = a(2) = 1, a(3) = 2; a(n) = a(a(n-1)-1) + a(n-a(n-3)-1) for n > 3.
%H A284523 Robert Israel, <a href="/A284523/b284523.txt">Table of n, a(n) for n = 1..10000</a>
%H A284523 Altug Alkan, <a href="/A284523/a284523.png">Plot for n=0..10^6</a>
%p A284523 a:= proc(n) option remember;
%p A284523 procname(procname(n-1)-1) + procname(n-procname(n-3)-1)
%p A284523 end proc:
%p A284523 a(1):= 1: a(2):= 1: a(3):= 2:
%p A284523 map(a, [$1..100]);
%t A284523 a[1] = a[2] = 1; a[3] = 2; a[n_] := a[n] = a[a[n - 1] - 1] + a[n - a[n - 3] - 1]; Array[a, 81] (* _Michael De Vlieger_, Mar 28 2017 *)
%Y A284523 Cf. A004001, A005185, A055748.
%K A284523 nonn,look
%O A284523 1,3
%A A284523 _Altug Alkan_ and _Robert Israel_, Mar 28 2017