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%I #98 Sep 08 2022 10:50:47
%S 0,1,1,3,6,25,86,416,1988,10640,57987,328956,1900321,11204350,
%T 67042778,406780346
%N Number of polyominoes (A000105) with perimeter 2n.
%C 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).
%C 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
%H Andrew Clarke, <a href="http://www.recmath.com/PolyPages/PolyPages/Isopolyos.html">Isoperimetrical Polyominoes</a>
%H Andrew Clarke, <a href="/A057730/a057730.gif">Picture from Andrew Clarke's page showing the polyominoes of perimeters 4, 6, 8 and 10.</a>
%H Gordon Hamilton, <a href="http://youtu.be/z0xUwJmUiFs">Grade 3 area and perimeter activity</a>
%H R. J. Mathar, <a href="/A057730/a057730.p10.txt">perimeter 10</a>
%H R. J. Mathar, <a href="/A057730/a057730.p12.txt">perimeter 12</a>
%H R. J. Mathar, <a href="/A057730/a057730_1.p14.txt">perimeter 14</a>
%H R. J. Mathar, <a href="/A057730/a057730_4.p16.txt">Illustrating perimeter 16, area <= 13</a>
%H R. J. Mathar, <a href="/A057730/a057730_4.p18.txt">Illustrating perimeter 18, area <= 13</a>
%H R. J. Mathar, <a href="/A057730/a057730_1.p20.txt">Illustrating perimeter 20, area <= 13</a>
%Y Cf. A000105, A002931, A057753, A266549 (same, but holes not allowed), column sums of A342243, A131487 (polyominoes by total number of edges).
%K nonn,nice,more
%O 1,4
%A _N. J. A. Sloane_, Oct 29 2000
%E Additional comments from _Barry Cipra_, Jun 08 2004
%E Link updated by _William Rex Marshall_, Dec 16 2009
%E a(9)-a(10) added by _Luca Petrone_, Jan 08 2016
%E a(1)-a(9) confirmed by _Bert Dobbelaere_, Oct 19 2018
%E a(10)-a(12) corrected and extended by _John Mason_, Jul 26 2021
%E a(13)-a(16) added by _John Mason_, Sep 08 2022
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