A113049 -id:A113049 - cp's OEIS frontend

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

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Paul Barry, Oct 11 2005

easy
nonn

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.

Cf. A039969, A113047, A113049.

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

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

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