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This Python program solves the problem recursively. It runs in 40ms.

Solution:The artwork consists of 33 pins.The position of the pins corresponds to the first 33 terms of sequence A005836 in OEIS [ https://oeis.org/A005836 ].

Here is a plot of the positions of the first 32 pins.

Aesthetically I wouldn’t have bothered with the 33rd pin.

MMA solution