In how many pieces a regular n-gon is cut into by its diagonals?
I need a general formula.
By inspection, I have the solution to some lower values of $n$.
For $n=3,4,5,6$ solutions are $1, 4, 11, 24$ respectively.
2026-03-28 18:17:09.1774721829
Number of Pieces a regular $n$-gon is cut into by its diagonals
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This is OEIS A007678, the second sequence when I plugged in your values. It goes $1, 4, 11, 24, 50, 80, 154, 220, 375, 444, 781, 952, 1456, 1696, 2500, 2466, 4029, 4500, 6175, 6820, 9086, 9024, 12926, 13988, 17875, 19180, 24129, 21480, 31900, 33856, 41416, 43792, 52921, 52956, 66675, 69996, 82954, 86800, 102050\dots $ An article (referenced in the OEIS entry) on the subject is here. There doesn't seem to be a simple formula.