%I
%S 1,1,0,2,0,1,0,0,0,0,0,2,0,2,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
%T 0,0,0,0,0,0,0,0,0,2,0,2,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N Binomial(4n,n)/(3n+1) mod 4.
%C It would appear that the behavior of this sequence is determined by values of the Jacobsthal numbers J(n)=A001045(n): a(n)=1 only if n=J(2k),k=0,1,...; a(n)=2 only if n=J(2k+3)+2J(2j), some k,j>=0, otherwise a(n)=0.
%t Table[Mod[Binomial[4n,n]/(3n+1),4],{n,0,120}] (* _Harvey P. Dale_, Mar 18 2018 *)
%Y Cf. A039969, A113047, A113049.
%K easy,nonn
%O 0,4
%A _Paul Barry_, Oct 11 2005
