A238823 -id:A238823 - 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).

A319323 a(n) is the number of column convex polyiamonds with n cells.

Original entry on oeis.org

2, 3, 6, 14, 36, 94, 246, 645, 1682, 4367, 11312, 29261, 75654, 195607, 505794, 1307977, 3382628, 8748288, 22625594, 58516858, 151343298, 391422104, 1012341602

Offset: 1

David Bevan, Sep 27 2018

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

			The only septiamonds that are not column convex are four rotations/reflections of a "7" shape. So a(7) = A001420(7) - 4 = 246.

Adam Gruber, Java program to count lattice animals.

Cf. A001420 (fixed polyiamonds), A238823 (row convex polyiamonds).

cp's OEIS Frontend

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

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