A001071 Number of one-sided chessboard polyominoes with n cells. (Formerly M0173 N0067)

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

Offset

1,1

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

Table of n, a(n) for n=1..23.

Joseph Myers, Chessboard polyominoes

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

Crossrefs

Cf. A001933, A121198.

Sequence in context: A134654 A198262 A085421 * A121198 A234599 A016544

Adjacent sequences: A001068 A001069 A001070 * A001072 A001073 A001074

Keyword

hard,nonn,more

Author

N. J. A. Sloane

Extensions

Extended by Joseph Myers, Oct 01 2011

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

Status

approved