Warren wanted to save money to purchase a new car. He started by saving​ $1 on the first of January. On the first of​ February, he saved ​$4. On the first of​ March, he saved ​$16. So on the first day of each​ month, he wanted to save four times as much as he did on the first day of the previous month. If Warren continues his savings​ pattern, how much will he need to save on the first day of ​October?