A001071 - OEIS

%I M0173 N0067 #34 Sep 06 2025 23:16:16

%S 2,1,4,10,36,108,392,1363,5000,18223,67792,252938,952540,3602478,

%T 13699554,52296713,200406388,770411478,2970401696,11482395526,

%U 44491881090,172766311857,672186650116

%N Number of one-sided chessboard polyominoes with n cells.

%C 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

%D W. F. Lunnon, personal communication.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Joseph Myers, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2010-November/013893.html">Chessboard polyominoes</a>

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

%F   O(n) = A000988(n),

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

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

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

%Y Cf. A001933, A121198.

%K hard,nonn,more

%O 1,1

%A _N. J. A. Sloane_

%E Extended by _Joseph Myers_, Oct 01 2011

%E a(18)-a(23) by _John Mason_, Jan 02 2014