Calculating if Capital Gain is Long Term

I am considering selling an asset, in this case, some shares of a stock (let say Stock X) that I purchased. It has recently ran up quite a bit since the purchase of it, and would like to sell some of the shares to diversify a bit. However, I would like to make sure the capital gains are taxed as long term capital gains, and my behavior is a bit funny in the beginning, so I wanted to make sure I am calculating the selling dates correctly. 

I purchased 20 shares on September 16, 2019. 
I purchased 5 shares on October 3, 2019.
total 25
I sold 5 shares on October 9, 2019. 
total 20
I sold 10 shares on February 4, 2020. 

total 10
I bought 10 shares on February 6, 2020. 

In the end, that leaves me with total 20 shares. 

I would assume that I can sell 10 shares on or after September 17, 2020 and have it count for long term capital gains, and then sell 10 shares on or after February 7, 2021 for long term capital gains. 

Is this correct? If not, why, and what would the dates be?