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Haskell, \$n=16\$ in about 9 minutes As observed by @xnor in the comments, we can break the problem down into two parts: generate polyominoes (where I reused a lot from here, then count the ways to distribute the remaining cubes. The symmetries are accounted for by using Burnside's lemma. So we need to know how many buildings of a given symmetric shape are ...


TI-BASIC (TI-84+), 1042 bytes "...


TikZ, 164 bytes \documentclass[tikz]{standalone}\begin{document}\tikz{\foreach\i in{0,120,240}\fill[rotate=\i](60:3)arc(60:0:3)--(0:10)arc(0:60:10);\fill circle(2)}\end{document}

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