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Number of maximally biased free polyominoes with n squares.
1

%I #27 Jul 09 2019 13:06:10

%S 1,1,2,1,1,11,8,3,1,79,36,8,2,540,164,31,4,3174,749,106,11,17443,3312,

%T 397,27

%N Number of maximally biased free polyominoes with n squares.

%C Define the bias of a polyomino to be the difference between the number of black squares and the number of white squares when chessboard coloring is applied to the polyomino. Maximally biased polyominoes of size n are those sharing the maximum value of bias among all polyominoes of n squares. For n = 4m + 1, for integer m, all maximally biased polyominoes may be built starting with a monomino and then successively adding "airplane" tetrominoes.

%H John Mason, <a href="/A234013/a234013.pdf">Chessboard coloured polyominoes and bias</a>

%H Herman Tulleken, <a href="https://www.researchgate.net/publication/333296614_Polyominoes">Polyominoes 2.2: How they fit together</a>, (2019).

%Y Cf. A000105, A106249, A001933, A234012.

%K nonn,more,nice

%O 1,3

%A _John Mason_, Dec 27 2013

%E More terms from _John Mason_, Jan 03 2015