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A216820 Number of polyominoes of site-perimeter n with 8-holes allowed.

%I A216820 #21 Oct 12 2023 11:04:47
%S A216820 1,0,2,4,12,32,110,340,1209,4272,16166,61848,246660,1004883,4209124,
%T A216820 18020832,78898047,352437205,1605225878,7445515638,35142033027,
%U A216820 168644213617,822311934788,4071431204506,20457850555113
%N A216820 Number of polyominoes of site-perimeter n with 8-holes allowed.
%C A216820 This sequence counts fixed connected (via common edges) polyominoes with given site-perimeter. The site-perimeter of a polyomino is the number of cells that are adjacent to it (via common edges). This sequence allows holes of any kind; A216819 allows holes but requires them to be connected to each other and to the exterior area via common corners; A216818 doesn't allow holes. - _Andrey Zabolotskiy_, Feb 02 2022
%H A216820 A. R. Conway and A. J. Guttmann, <a href="https://doi.org/10.1088/0305-4470/28/4/015">On two-dimensional percolation</a>, J. Phys. A: Math. Gen., 28 (1995), 891-904. See Table 2.
%H A216820 J. Fortier, A. Goupil, J. Lortie and J. Tremblay, <a href="https://doi.org/10.1016/j.tcs.2012.02.032">Exhaustive generation of gominoes</a>, Theoretical Computer Science, 502 (2013), 76-87. See Table 1, beware of the typo in a(15).
%e A216820 The only polyomino with site-perimeter 4 is a single cell.
%e A216820 No polyominoes have site-perimeter 5.
%e A216820 a(6) = 2: the domino, rotated (or reflected) in 2 possible ways.
%e A216820 a(7) = 4: the L-tromino, rotated in 4 ways.
%e A216820 a(8) = 12: the X-pentomino; the square tetromino; the straight tromino, rotated in 2 ways; the T-tetromino, rotated in 4 ways; the skew tetromino, rotated and reflected in 4 ways.
%Y A216820 Cf. A216818 (no holes), A216819 (holes connected by corners); A001168 (by area), A057730 (by perimeter); A366443 (free).
%K A216820 nonn,more
%O A216820 4,3
%A A216820 _N. J. A. Sloane_, Sep 20 2012
%E A216820 a(15) corrected, a(16)-a(28) from Conway & Guttmann added by _Andrey Zabolotskiy_, Feb 02 2022