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%I #11 Sep 08 2022 08:46:22
%S 1,1,1,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,7,7,7,8,8,8,8,8,8,9,9,9,
%T 10,10,10,10,11,11,11,12,12,12,12,12,13,13,13,14,14,14,14,15,15,15,16,
%U 16,16,16,16,16,16,17,17,17,18,18,18,18,19,19,19,20,20
%N a(1)=a(2)=a(3)=1; a(n) = a(n-2*a(n-1))+a(n-1-2*a(n-2)) for n > 3.
%C This sequence increases slowly, and each term repeats at least three times.
%C If k is not a power of 2, then k appears in this sequence the same number of times as it appears in A081832. Otherwise, it appears exactly one additional time.
%H Nathan Fox, <a href="/A316626/b316626.txt">Table of n, a(n) for n = 1..10000</a>
%H A. Erickson, A. Isgur, B. W. Jackson, F. Ruskey and S. M. Tanny, <a href="http://webhome.cs.uvic.ca/~ruskey/Publications/MetaFib/ConollyLikeMay14.pdf">Nested recurrence relations with Conolly-like solutions</a>, See Conjecture 5.1.
%F a(n+1)-a(n)=1 or 0.
%F a(n)/n -> C=1/4.
%p A316626:=proc(n) option remember: if n <= 0 then 0: elif n = 1 then 1: elif n = 2 then 1: elif n = 3 then 1: else A316626(n-2*A316626(n-1)) + A316626(n-1-2*A316626(n-2)): fi: end:
%o (Magma) [n le 3 select 1 else Self(n-2*Self(n-1))+Self(n-1-2*Self(n-2)): n in [1..100]]; // _Vincenzo Librandi_, Jul 09 2018
%o (GAP) a:=[1,1,1];; for n in [4..80] do a[n]:=a[n-2*a[n-1]]+a[n-1-2*a[n-2]]; od; a; # _Muniru A Asiru_, Jul 09 2018
%Y Cf. A005185, A046699, A081832.
%K nonn
%O 1,4
%A _Nathan Fox_ and _Altug Alkan_, Jul 08 2018
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