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Number of n-celled polyominoes which are of square type.
3

%I #28 Mar 21 2024 21:01:16

%S 1,0,1,1,6,7,25,80,255,795,2919,10378,36590,130716,480773,1774714,

%T 6543633,24208803,90331307,339178346,1277308160,4819109576

%N Number of n-celled polyominoes which are of square type.

%H R. J. Mathar, <a href="http://www.vixra.org/abs/1905.0474">Corrigendum to "Polynomino enumeration results (Parkin et al, SIAM Fall Meeting 1967)"</a>, vixra:1905.0474

%H T. R. Parkin, L. J. Lander, and D. R. Parkin, <a href="/A000104/a000104.pdf">Polyomino Enumeration Results</a>, presented at SIAM Fall Meeting, 1967, and accompanying letter from T. J. Lander (annotated scanned copy). See page 21. The 15th entry is not included because their value for A000105(15) was incorrect.

%F a(n)+A259087(n) = A000105(n).

%e a(7) = 25 with 7 free 7-ominoes with a 3x3 hull and 18 with 4x4 hull. a(8) = 80 with 3 free 8-ominoes with a 3x3 hull and 77 with a 4x4 hull. a(9) = 255 with 1 free 9-omino in a 3x3 hull, 181 in a 4x4 hull and 73 in a 5x5 hull. - _R. J. Mathar_, May 24 2019

%Y Cf. A259087, A268311, A000105.

%K nonn,more

%O 1,5

%A _N. J. A. Sloane_, Jun 18 2015

%E a(15)-a(16) from _R. J. Mathar_, May 22 2019

%E a(17) from _R. J. Mathar_, May 27 2019

%E a(18)-a(22) from _John Mason_, Nov 19 2021