A001071 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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,