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%I #22 Sep 20 2024 06:06:29
%S 1,1,2,6,17,58,191,700,2515,9623,36552,143761,564443,2259905,9057278,
%T 36705846,149046429,609246350,2495727647,10267016450,42322763940,
%U 174974139365
%N Number of achiral polyominoes with n cubical cells of the regular tiling with Schläfli symbol {4,3,4} (or polycubes).
%C A000162 but with both copies of each mirror-image deleted.
%C An achiral polyomino is identical to its reflection. Many of these achiral polyominoes do not have a plane of symmetry. For example, the hexomino with cell centers (0,0,0), (0,0,1), (0,1,1), (1,1,1), (1,2,1), and (1,2,2) has a center of symmetry at (1/2,1,1) but no plane of symmetry. The decomino with cell centers (0,0,0), (0,0,1), (0,1,1), (0,2,1), (0,2,2), (1,0,2), (1,1,2), (1,1,1), (1,1,0), and (1,2,0) has no plane or center of symmetry. - _Robert A. Russell_, Mar 21 2024
%H G. Thimm, <a href="/A007741/a007741.pdf">Emails to N. J. A. Sloane, Sep. 1994</a>
%F a(n) = A000162(n) - 2*A371397(n) = A038119(n) - A371397(n). - _Robert A. Russell_, Mar 21 2024
%Y A038119 = (A007743+A000162)/2, A007743 = 2*A038119 - A000162, A000162 = 2*A038119 - A007743.
%Y Cf. A000162 (oriented), A038119 (unoriented), A371397 (chiral), A001931 (fixed).
%K nonn,nice
%O 1,3
%A Arlin Anderson (starship1(AT)gmail.com)
%E a(13)-a(16) from Herman Jamke (hermanjamke(AT)fastmail.fm), May 05 2007
%E Changed "symmetric" to "mirror-symmetric" in the title by _George Sicherman_, Feb 21 2018
%E Changed "mirror-symmetric" to "achiral" in the title to ensure that a plane of symmetry is not required. - _Robert A. Russell_, Mar 21 2024
%E a(17)-a(22) from _John Mason_, Sep 19 2024