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 A157685 #6 Jun 02 2025 01:25:41
%S A157685 0,0,1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,5,6,6,7,7,7,8,8,8,9,9,9,10,10,10,
%T A157685 11,11,11,12,12,12,13,13,13,14,14,14,15,15,16,16,16,17,17,17,17,18,18,
%U A157685 18,19,19,19,20,20,20,21,21,21,22,22,22,23,23,23,24,24,24,25,25,26,26,26
%N A157685 a(n)=#{1<=k<=n : [K(k),K(k+1)]=[2,1]} where K=A000002.
%C A157685 Presumably a(n)=n/3+o(n)
%F A157685 a(n)=sum(k=1,n,(1-K(k))*(K(k+1)-K(k))) where K(k)=A000002(k).
%o A157685 (PARI) a(n)=sum(k=1,n,if(abs(A000002(k)-2)+abs(A000002(k+1)-1),0,1))
%Y A157685 Cf. A157684, A157686, A157687
%K A157685 nonn
%O A157685 1,6
%A A157685 _Benoit Cloitre_, Mar 04 2009