A194596
Number of free polyplets with n cells that are not polyominoes.
Original entry on oeis.org
0, 1, 3, 17, 82, 489, 2923, 18401, 116848, 753726, 4898579, 32085696, 211398614, 1400292492, 9318028028, 62259251309, 417496576187
Offset: 1
XX...X.X..X.. (the 3 for n=3)
..X...X....X.
............X
a(3) = 5 - 2 = 3
a(4) = 22 - 5 = 17
a(5) = 94 - 12 = 82
- Eric Weisstein's World of Mathematics, Polyplet.
A319321
a(n) is the number of d+/d- diagonally convex polyplets (polyominoes which need only touch at corners) with n cells.
Original entry on oeis.org
1, 4, 20, 108, 600, 3368, 18968, 106906, 602532, 3395402, 19131460, 107788900, 607274848
Offset: 1
The only tetraplets that are not d+ diagonally convex are two animals consisting of a horizontal domino and a vertical domino joined at a corner. So a(4) = A006770(4) - 2 = 108.
Cf.
A006770 (fixed polyplets),
A187077 (row convex polyplets),
A187276 (d+/d- diagonally convex polyominoes).
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