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A330416 a(n) = (number of times a(n-2) has already appeared) + (number of times a(n-3) has already appeared), starting with a(n) = n for n<3.

%I A330416 #9 Dec 14 2019 19:26:07
%S A330416 0,1,2,2,3,4,3,3,4,6,5,3,2,5,7,5,4,4,7,8,6,3,3,8,12,8,4,4,9,12,7,3,5,
%T A330416 10,11,5,2,6,9,7,5,6,10,10,7,6,8,10,9,8,7,8,12,12,10,8,9,12,11,9,7,7,
%U A330416 13,16,9,2,7,11,14,12,4,7,13,17,12,3,8,15,16,9
%N A330416 a(n) = (number of times a(n-2) has already appeared) + (number of times a(n-3) has already appeared), starting with a(n) = n for n<3.
%C A330416 This sequence is a variant of A330332.
%C A330416 This sequence appears to diverge much more slowly than A330332.
%H A330416 Rémy Sigrist, <a href="/A330416/a330416.txt">C program for A330416</a>
%H A330416 Rémy Sigrist, <a href="/A330416/a330416.png">Density plot of the first 100000000 terms</a>
%e A330416 a(0) = 0.
%e A330416 a(1) = 1.
%e A330416 a(2) = 2.
%e A330416 For n = 3:
%e A330416 - a(1) = 1 has appeared once, a(0) = 0 has appeared once,
%e A330416 - hence a(3) = 1+1 = 2.
%e A330416 For n = 4:
%e A330416 - a(2) = 2 has appeared twice, a(1) = 1 has appeared once,
%e A330416 - hence a(4) = 2+1 = 3.
%t A330416 Nest[Append[#, Count[#, #[[-2]] ] + Count[#, #[[-3]] ]] &, {0, 1, 2}, 77] (* _Michael De Vlieger_, Dec 14 2019 *)
%o A330416 (C) See Links section.
%Y A330416 Cf. A330332.
%K A330416 nonn
%O A330416 0,3
%A A330416 _Rémy Sigrist_, Dec 14 2019