Trying to derive an equation to express number of carps in play I play magic the gathering. This is the situation, without needing to know the rules: You gain one total available "mana" per turn. So available mana = number of turns passed. Your only creature, of which you have inexhaustible copies, costs 5 mana. You can play as many per turn as you have mana for. So on turn five, you can play one. The same is true on turn 6, since 6 % 5 = 1. So by the end of turn 6, you have two of these creatures in play: one from the previous turn, and one that you've just played. At the end of turn 7, there will be 3. On turn ten, you can start playing two per turn, since 10 / 5 = 2. How can I express the number of creatures played in this manner as a function of the number of turns that have passed for me?

Here's a way of writing it you might like: define $m =\lfloor t/5 \rfloor$, and we have $$ n = 5\frac{m(m+1)}{2} + m(t \bmod 5) $$ where $t \bmod 5$ is the remiander of the division $t \div 5$.