This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A316626 #11 Sep 08 2022 08:46:22 %S A316626 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 A316626 10,10,10,10,11,11,11,12,12,12,12,12,13,13,13,14,14,14,14,15,15,15,16, %U A316626 16,16,16,16,16,16,17,17,17,18,18,18,18,19,19,19,20,20 %N A316626 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 A316626 This sequence increases slowly, and each term repeats at least three times. %C A316626 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 A316626 Nathan Fox, <a href="/A316626/b316626.txt">Table of n, a(n) for n = 1..10000</a> %H A316626 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 A316626 a(n+1)-a(n)=1 or 0. %F A316626 a(n)/n -> C=1/4. %p A316626 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 A316626 (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 A316626 (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 A316626 Cf. A005185, A046699, A081832. %K A316626 nonn %O A316626 1,4 %A A316626 _Nathan Fox_ and _Altug Alkan_, Jul 08 2018