A113048 Binomial(4n,n)/(3n+1) mod 4.

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, 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, 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

Offset: 0

Author

Paul Barry, Oct 11 2005

Keywords

• easy
• nonn

Comments

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.

Crossrefs

Cf. A039969, A113047, A113049.

Programs

Mathematica

Table[Mod[Binomial[4n,n]/(3n+1),4],{n,0,120}] (* Harvey P. Dale, Mar 18 2018 *)