login
a(n)=#{1<=k<=n : [K(k),K(k+1)]=[2,1]} where K=A000002
3

%I #4 Mar 30 2012 18:39:28

%S 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 11,11,11,12,12,12,13,13,13,14,14,14,15,15,16,16,16,17,17,17,17,18,18,

%U 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 a(n)=#{1<=k<=n : [K(k),K(k+1)]=[2,1]} where K=A000002

%C Presumably a(n)=n/3+o(n)

%F a(n)=sum(k=1,n,(1-K(k))*(K(k+1)-K(k))) where K(k)=A000002(k).

%o (PARI) a(n)=sum(k=1,n,if(abs(A000002(k)-2)+abs(A000002(k+1)-1),0,1))

%Y Cf. A157684, A157686, A157687

%K nonn

%O 1,6

%A _Benoit Cloitre_, Mar 04 2009