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Jelly, 34 bytes
Ẏ9ḟƑƇṭ8ドルṢ€ȯW)ẎQ
;þ;Z,ドルƝ€ẎW€çƬ$ṪLo1
A dyadic link taking the dimensions as the left and right arguments and returning an integer. The TIO footer generates a 4x4 table similar to the one in the question; the argument for the footer is the size of the table to generate.
Full explanation to follow, but in brief this generates all possible dominoes and then builds all possible lists of those dominoes that don’t have any overlaps. It would be fairly straightforward to extend this to larger polyominoes (though the first part of the code would be a bit more complex); here’s an initial attempt.
Jelly, 34 bytes
Ẏ9ḟƑƇṭ8ドルṢ€ȯW)ẎQ
;þ;Z,ドルƝ€ẎW€çƬ$ṪLo1
A dyadic link taking the dimensions as the left and right arguments and returning an integer. The TIO footer generates a 4x4 table similar to the one in the question; the argument for the footer is the size of the table to generate.
Full explanation to follow, but in brief this generates all possible dominoes and then builds all possible lists of those dominoes that don’t have any overlaps. It would be fairly straightforward to extend this to larger polyominoes (though the first part of the code would be a bit more complex).
Jelly, 34 bytes
Ẏ9ḟƑƇṭ8ドルṢ€ȯW)ẎQ
;þ;Z,ドルƝ€ẎW€çƬ$ṪLo1
A dyadic link taking the dimensions as the left and right arguments and returning an integer. The TIO footer generates a 4x4 table similar to the one in the question; the argument for the footer is the size of the table to generate.
Full explanation to follow, but in brief this generates all possible dominoes and then builds all possible lists of those dominoes that don’t have any overlaps. It would be fairly straightforward to extend this to larger polyominoes (though the first part of the code would be a bit more complex); here’s an initial attempt.
Jelly, 34 bytes
Ẏ9ḟƑƇṭ8ドルṢ€ȯW)ẎQ
;þ;Z,ドルƝ€ẎW€çƬ$ṪLo1
A dyadic link taking the dimensions as the left and right arguments and returning an integer. The TIO footer generates a 4x4 table similar to the one in the question; the argument for the footer is the size of the table to generate.
Full explanation to follow, but in brief this generates all possible dominoes and then builds all possible lists of those dominoes that don’t have any overlaps. It would be fairly straightforward to extend this to larger polyominoes (though the first part of the code would be a bit more complex).