You're on the right track....we have a pattern that you found as
Term 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
3, 27, 24, 3, 21, 18, 3, 15, 12, 3, 9, 6, 3, [3, 0, 3] , [ 3, 0, 3], ]3, 0 , 3]
Notice that......starting with the 14th term we have the repeating pattern 3,0,3
Notice that after this ( term number + 2) ] / 3 gives us what we need to determine the 2016th term
Notice that
(14 + 2) / 3 = 16/3 = 5 + 1/3 = 1st number in the pattern = 3
(15 + 2) / 3 = 17/3 = 5 + 2/3 = 2nd number in the pattern = 0
(16 + 2) / 3 = 18/3 = 6 whole number result gives us the 3rd number in the pattern = 3
So....to determine the 2016th term we have
(2016 + 2 ] / 3 = 2018 / 3 = = 672 + 2/3 = 2nd number in pattern = 0