Formula for 12 days of Christmas?

If you were to substitute exercises for gifts in the song 12 days of christmas. And then perform them for every mention in the verse. For example..

• on the 12th day 12 pushups=12
• on the 11th day 11 situps=22
• on the 10th day 10 jumping jacks=30

Is there a formula to express this?

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I'm not sure what you mean. Are you asking about something like $(13-n)\cdot n$?
To derive this, see that $n$-th verse is repeated $(13-n)$ times, so if you do the exercise associated to $n$-th verse $n$ times each time it is repeated, you do it $(13-n)\cdot n$ times in total.