A057730 Number of polyominoes (A000105) with perimeter 2n.

0, 1, 1, 3, 6, 25, 86, 416, 1988, 10640, 57987, 328956, 1900321, 11204350, 67042778, 406780346

Offset: 1

Author

N. J. A. Sloane, Oct 29 2000

Keywords

• nonn
• nice
• more

Comments

Does this include polyominoes with holes? - Franklin T. Adams-Watters, Sep 12 2006. Answer from R. J. Mathar: Yes! See the illustrations in the links (e.g. perimeter 16, area 7, No 81 or perimeter 16, area 8, No 174).

All lines (sides of cells which are not common to a pair of cells) contribute to the perimeter, including the interior sides of cavities and holes. - R. J. Mathar, Feb 19 2021

Links

• Andrew Clarke, Isoperimetrical Polyominoes
• Andrew Clarke, Picture from Andrew Clarke's page showing the polyominoes of perimeters 4, 6, 8 and 10.
• Gordon Hamilton, Grade 3 area and perimeter activity
• R. J. Mathar, perimeter 10
• R. J. Mathar, perimeter 12
• R. J. Mathar, perimeter 14
• R. J. Mathar, Illustrating perimeter 16, area <= 13
• R. J. Mathar, Illustrating perimeter 18, area <= 13
• R. J. Mathar, Illustrating perimeter 20, area <= 13

Crossrefs

Cf. A000105, A002931, A057753, A266549 (same, but holes not allowed), column sums of A342243, A131487 (polyominoes by total number of edges).

Extensions

Additional comments from Barry Cipra, Jun 08 2004

Link updated by William Rex Marshall, Dec 16 2009

a(9)-a(10) added by Luca Petrone, Jan 08 2016

a(1)-a(9) confirmed by Bert Dobbelaere, Oct 19 2018

a(10)-a(12) corrected and extended by John Mason, Jul 26 2021

a(13)-a(16) added by John Mason, Sep 08 2022