A234013 Number of maximally biased free polyominoes with n squares.

1, 1, 2, 1, 1, 11, 8, 3, 1, 79, 36, 8, 2, 540, 164, 31, 4, 3174, 749, 106, 11, 17443, 3312, 397, 27

Offset: 1

Author

John Mason, Dec 27 2013

Keywords

• nonn
• more
• nice

Comments

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.

Links

• John Mason, Chessboard coloured polyominoes and bias
• Herman Tulleken, Polyominoes 2.2: How they fit together, (2019).

Crossrefs

Cf. A000105, A106249, A001933, A234012.

Extensions

More terms from John Mason, Jan 03 2015