A319324 -id:A319324 - cp's OEIS frontend

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

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).

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).

A340341 Number of polymings with n cells, distinguishing mirror images.

Original entry on oeis.org

1, 3, 16, 129, 1009, 8997, 80816, 746483, 6983847, 66146105, 632186200, 6089173570

Offset: 1

George Sicherman, Jan 04 2021

A polyming is a generalized polyiamond whose cells may be joined at corners as well as at edges. I introduced the term in 2010. In A319324 and elsewhere, David Bevan calls these shapes "polyglasses." In A239658, Abe Wits and Ragnar Groot Koerkamp call them simply "triangular polyplets."

			a(3)=16, because there are 11 two-sided 3-mings (identifying mirror images), and 5 of them are chiral.  See the link above.

G. L. Sicherman, Catalogue of Polymings

Cf. A239658, A319324.

a(11) and a(12) from Aaron N. Siegel, May 22 2022

cp's OEIS Frontend

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

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Formula

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A340341 Number of polymings with n cells, distinguishing mirror images.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions