A001071 Number of one-sided chessboard polyominoes with n cells.

2, 1, 4, 10, 36, 108, 392, 1363, 5000, 18223, 67792, 252938, 952540, 3602478, 13699554, 52296713, 200406388, 770411478, 2970401696, 11482395526, 44491881090, 172766311857, 672186650116

Offset: 1

Author

N. J. A. Sloane

Keywords

• hard
• nonn
• more

Comments

Two polyominoes cut from a chessboard are considered the same for this sequence if the shapes of the polyominoes are related by a rotation or translation, and the colorings are related by any symmetry including a reflection. - Joseph Myers, Oct 01 2011

References

• W. F. Lunnon, personal communication.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Joseph Myers, Chessboard polyominoes

Crossrefs

Cf. A001933, A121198.

Formula

a(n) = 2*O(n) - M(n) - 2*(R90(n) + R180(n)), where:

O(n)=A000988(n),

for even n, M(n) = A234006(n/2), otherwise 0,

for n multiple of 4, R90(n) = A234007(n/4), otherwise 0,

for even n, R180(n) = A234008(n/2), otherwise 0

Extensions

Extended by Joseph Myers, Oct 01 2011

a(18)-a(23) by John Mason, Jan 02 2014