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A284511 a(1) = 1, a(2) = 2, a(3) = 2; a(n) = a(a(n-1)-1) + a(n-a(n-2)) for n > 3.

%I A284511 #25 Mar 29 2022 02:35:50
%S A284511 1,2,2,3,4,4,4,5,7,8,7,7,8,8,8,9,12,14,12,11,15,15,13,14,15,15,15,16,
%T A284511 16,16,16,17,21,23,23,23,23,23,24,25,26,27,27,27,29,28,29,27,26,28,30,
%U A284511 30,29,30,31,31,31,31,32,32,32,32,32,33,38,44,43,41,40,40,40,41,46,50
%N A284511 a(1) = 1, a(2) = 2, a(3) = 2; a(n) = a(a(n-1)-1) + a(n-a(n-2)) for n > 3.
%H A284511 Altug Alkan, <a href="/A284511/b284511.txt">Table of n, a(n) for n = 1..20000</a>
%H A284511 Altug Alkan, <a href="/A284511/a284511.png">Scatterplot of A284511</a>
%H A284511 Altug Alkan, <a href="/A284511/a284511_1.png">Scatterplot of 2*a(n)-n</a>
%F A284511 a(n) = a(a(n-1)-1) + a(n-a(n-2)), with a(1) = 1, a(2) = 2, a(3) = 2.
%e A284511 a(4) = 3 because a(4) = a(a(3) - 1) + a(4 - a(2)) = a(1) + a(2) = 3.
%p A284511 a:= proc(n) option remember;
%p A284511   procname(procname(n-1)-1)+procname(n-procname(n-2))
%p A284511 end proc:
%p A284511 a(1):= 1: a(2):= 2: a(3):= 2:
%p A284511 map(a, [$1..100]); # _Robert Israel_, Mar 28 2017
%t A284511 a[1]=1; a[2]=a[3]=2; a[n_] := a[n] = a[a[n-1]-1] + a[n-a[n-2]]; Array[a, 74] (* _Giovanni Resta_, Mar 28 2017 *)
%o A284511 (PARI) a=vector(1000); a[1]=1; a[2]=a[3]=2; for(n=4, #a, a[n]=a[a[n-1]-1]+a[n-a[n-2]]); a
%o A284511 (Sage)
%o A284511 @CachedFunction
%o A284511 def a(n): # A284511
%o A284511     if (n<4): return 2 - bool(n==1)
%o A284511     else: return  a(a(n-1)-1) + a(n-a(n-2))
%o A284511 [a(n) for n in (1..80)] # _G. C. Greubel_, Mar 28 2022
%Y A284511 Cf. A004001, A005185, A005229, A055748, A070867, A226222.
%K A284511 nonn
%O A284511 1,2
%A A284511 _Altug Alkan_, Mar 28 2017