Indeed this is a distribution.
In fact, as you describe it, this is a liquidating distribution (for that partner). A liquidating distribution is when a partner's interest in the partnership is terminated in exchange for his share of the value of the partnership.
At http://www.irs.gov/businesses/partnerships/article/0,,id=134693,00.html there is a discussion of distributions including a section on liquidating distributions.
See also http://www.irs.gov/publications/p541/ar02.html#en_US_publink1000104228
I hope this helps to know it is a distribution that liquidates the partner's interest.
One other question. Do we calculate the # XXXXX days he was a partner for his share of the profits?
Yes, that is an often used method to determine the share of profits - to prorate the annual net inocme and expenses. Some professional tax software will allow you to enter the dates of change in ownership and will make the computations.
The most accurate method would be to actually have separate accounting periods with 1/4 shares up to the date of liquidation adn 1/3 shares for the period after one partner liquidated. Most accounting software will allow printing reports for each period. In that case you would usually override the dollar amounts allocated to wach partner.
I hope this helps to clarify for you.