A formula for a sequence which has three odds and then three evens, alternately We know that triangular numbers are 1, 3, 6, 10, 15, 21, 28, 36... where we have alternate two odd and two even numbers. This sequence has a simple formula $a_n=n(n+1)/2$. What would be an example of a sequence, described by a similar algebraic formula, which has three odds and then three evens, alternately? Ideally, it would be described by a polynomial of low degree.

The sequence $$n \mapsto 4n^6+n^5+6n^3+4n \pmod 7$$ for $n \geq 1$ gives $$1,1,1,0,0,0,1,1,1,0,0,0,\ldots.$$