A131482 a(n) is the number of n-celled polyominoes with perimeter 2n+2.

1, 1, 2, 4, 11, 27, 83, 255, 847, 2829, 9734, 33724, 118245, 416816, 1478602, 5267171, 18840144, 67611472, 243378415, 878407170, 3178068821, 11523323634, 41865833602, 152382134767

Offset: 1

Author

Tanya Khovanova, Jul 27 2007

Keywords

• hard
• more
• nonn

Comments

2n+2 is the maximal perimeter of an n-celled polyomino. a(n) is the number of n-celled polyominoes that have a tree as their connectedness graph (vertices of this graph correspond to cells and two vertices are connected if the corresponding cells have a common edge).

Links

• Andrew Clarke, Isoperimetrical Polyominoes, The Poly Pages.
• Herman Tulleken, Polyominoes 2.2: How they fit together, (2019).

Crossrefs

Cf. A000105, A057730. Diagonal of A342243.

A359522 counts only polyominoes with holes.

A002013 counts only unbranched polyominoes.

A038142 is the analog for polyhexes.

Formula

a(n) <= A000105(n), a(n) <= A057730(n+1).

a(n) >= A000602(n) [see comment on edge graph trees]. - R. J. Mathar, Mar 08 2021

Extensions

a(14)-a(16) from David Radcliffe, Dec 25 2017

a(17) from David Radcliffe, Dec 26 2017

a(18)-a(24) from John Mason, Dec 11 2021