A057730 - OEIS

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A057730

Number of polyominoes (A000105) with perimeter 2n.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

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

Table of n, a(n) for n=1..16.

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