A319325 -id:A319325 - cp's OEIS frontend

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

David Bevan, Sep 18 2018

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.

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

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.

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

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

A319326 a(n) is the number of column convex polyglasses (polyiamonds which need only touch at corners) with n cells.

Original entry on oeis.org

2, 12, 84, 612, 4532, 33762, 252106, 1884120, 14084674, 105295512, 787178752

Offset: 1

David Bevan, Sep 27 2018

A polyglass is column convex if the intersection of its interior with any vertical line through the centers of the cells is connected.

			There are four triglasses that are not column convex. So a(2) = A319324(3) - 4 = 84.

Adam Gruber, Java program to count lattice animals.

Cf. A319324 (fixed polyglasses), A319325 (row convex polyglasses), A319323 (column convex polyiamonds).

cp's OEIS Frontend

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

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