If an employer contributed to a 401K for one month in 2018 how can I maximize my tax deductions with IRA contribution?

It depends on your Modified Adjusted Gross Income.

As you have a 401(k) at work, even for one month, you are considered as covered by a retirement plan at work in 2018.

To determine if you can deduct an IRA contribution, please read this IRS document:

https://www.irs.gov/retirement-plans/plan-participant-employee/2018-ira-contribution-and-deduction-l...