A319326 -id:A319326 - 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

A319325 a(n) is the number of row convex polyglasses (polyiamonds which need only touch at corners) with n cells.

Original entry on oeis.org

2, 10, 52, 276, 1470, 7838, 41798, 222902, 1188696, 6339088, 33805118, 180276062, 961376842, 5126833922, 27340398612, 145800977348, 777527983398, 4146404063814, 22111958704510, 117918733974142, 628837454333128, 3353466668484240, 17883379272566534, 95368550166928198

Offset: 1

David Bevan, Sep 27 2018

nonn

			The only diglasses that are not row convex are "two mountains" and its 180-degree rotation. So a(2) = A319324(2) - 2 = 10.

Adam Gruber, Java program to count lattice animals.

Cf. A319324 (fixed polyglasses), A319326 (column convex polyglasses), A238823 (row convex polyiamonds).

Rest@CoefficientList[Series[(2z(1+z)(1-z)^3)/(1-7z+9z^2+z^3-9z^4+3z^5),{z,0,20}],z]

G.f.: (2*z*(1+z)*(1-z)^3)/(1-7z+9z^2+z^3-9z^4+3z^5).

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions