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A113048
Binomial(4n,n)/(3n+1) mod 4.
1
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
0,4
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.
MATHEMATICA
Table[Mod[Binomial[4n, n]/(3n+1), 4], {n, 0, 120}] (* Harvey P. Dale, Mar 18 2018 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 11 2005
STATUS
approved