A319324 a(n) is the number of fixed polyglasses (polyiamonds which need only touch at corners) with n cells.

2, 12, 88, 710, 6054, 53500, 484784, 4475010, 41902626, 396838992, 3793117200, 36534684066

Offset: 1

Author

David Bevan, Sep 18 2018

Keywords

• nonn
• more
• hard

Comments

Polyglasses are to polyiamonds (A001420) as polyplets (A006770) are to polyominoes (A001168). The name derives from the 2-celled animal (diglass) which looks like an hourglass.

Examples

			a(2) = 12: three rotations of a diamond, three rotations of an hourglass and six rotations of "two mountains".
		

Links

• David Bevan, The 88 fixed triglasses.
• Rebecca M. Bowen, Sadie Pruitt, and Douglas A. Torrance, Properties of regular Tangles, arXiv:2405.20793 [math.CO], 2024. See p. 2.
• Adam Gruber, Java program to count lattice animals.

Crossrefs

Cf. A001420 (fixed polyiamonds), A319325 (row convex polyglasses), A319326 (column convex polyglasses).

Extensions

a(12) from Aaron N. Siegel, May 22 2022