The OEIS is supported by the many generous donors to the OEIS Foundation.

a(n) is the number of d+/d- diagonally convex polyplets (polyominoes which need only touch at corners) with n cells.

0

`%I #10 Oct 27 2018 03:27:54
`

`%S 1,4,20,108,600,3368,18968,106906,602532,3395402,19131460,107788900,
`

`%T 607274848
`

`%N a(n) is the number of d+/d- diagonally convex polyplets (polyominoes which need only touch at corners) with n cells.
`

`%C A polyplet is d+ [d-] diagonally convex if the intersection of its interior with any line of slope 1 [-1] through the centers of the cells is connected.
`

`%H Adam Gruber, <a href="https://devweb3000.cis.strath.ac.uk/~xpb16190/LatticeAnimals/LatticeAnimals.jar">Java program to count lattice animals</a>.
`

`%e 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.
`

`%Y Cf. A006770 (fixed polyplets), A187077 (row convex polyplets), A187276 (d+/d- diagonally convex polyominoes).
`

`%K nonn,more
`

`%O 1,2
`

`%A _David Bevan_, Sep 27 2018
`