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A081832 a(1)=a(2)=1, a(n) = a(n+1-2*a(n-1)) + a(n-2*a(n-2)).

%I A081832 #36 Aug 01 2019 10:43:49
%S A081832 1,1,2,2,2,3,3,3,4,4,4,4,5,5,5,6,6,6,6,7,7,7,8,8,8,8,8,9,9,9,10,10,10,
%T A081832 10,11,11,11,12,12,12,12,12,13,13,13,14,14,14,14,15,15,15,16,16,16,16,
%U A081832 16,16,17,17,17,18,18,18,18,19,19,19,20,20,20,20,20,21,21,21,22,22,22
%N A081832 a(1)=a(2)=1, a(n) = a(n+1-2*a(n-1)) + a(n-2*a(n-2)).
%C A081832 Unlike the Hofstadter Q-sequence, this one seems to be an increasing sequence.
%C A081832 Sequence increases slowly and each term repeats at least three times except at the start. - _Altug Alkan_, Jun 07 2018
%H A081832 Muniru A Asiru, <a href="/A081832/b081832.txt">Table of n, a(n) for n = 1..10000</a>
%H A081832 Altug Alkan, <a href="/A081832/a081832_1.pdf">Proof of Slowness</a>
%F A081832 Conjectures: a(n)/n -> C=1/4; a(n+1)-a(n)=1 or 0, first differences are 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, ....
%F A081832 a(n+1)-a(n)=1 or 0, see Links section for proof. - _Altug Alkan_, Jun 07 2018
%p A081832 a:=proc(n) option remember: if n<3 then 1 else procname(n+1-2*procname(n-1))+procname(n-2*procname(n-2)) fi; end; seq(a(n),n=1..80); # _Muniru A Asiru_, Jun 06 2018
%t A081832 a[1] = a[2] = 1; a[n_] := a[n] = a[n + 1 - 2 a[n - 1]] + a[n - 2 a[n - 2]]; Array[a, 80] (* _Robert G. Wilson v_, Jun 13 2018 *)
%o A081832 (GAP) a:=[1,1];; for n in [3..80] do a[n]:=a[n+1-2*a[n-1]]+a[n-2*a[n-2]]; od; a; # _Muniru A Asiru_, Jun 06 2018
%Y A081832 Cf. A005185.
%K A081832 nonn,easy
%O A081832 1,3
%A A081832 _Benoit Cloitre_, Apr 10 2003