# Can this sequence be expressed with a closed-form formula?

1, 3, 5, 7, 9, 13, 17, 21, 25, 31, 37, 43, 49…

So if you don't count the first number the sequence is +2 for four times. After that it changes to +4 for four times, then +6, +8 and so on, all for four times.

• Your sequence is unclear. How many times is it $+6$? How many times is it $+8$? Etc. Also $37$ followed by $49$ seems wrong as that is $+12$. Please clarify your question. – Ian Miller Sep 17 '16 at 8:20

OEIS has a few closed-form formulas, including: $$a_n = \frac{2n(n + 2) + (-1)^n - 4\sin(\frac{n\pi}{2}) + 7}{8}$$