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

1,1

Links

Table of n, a(n) for n=1..24.

Adam Gruber, Java program to count lattice animals.

Formula

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A353289 A307208 A075436 * A361805 A344576 A360317

Adjacent sequences: A319322 A319323 A319324 * A319326 A319327 A319328

Keyword

nonn

Author

David Bevan, Sep 27 2018

Status

approved