This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A007743 #26 May 25 2025 01:59:10
%S A007743 1,1,2,6,17,58,191,700,2515,9623,36552,143761,564443,2259905,9057278,
%T A007743 36705846,149046429,609246350,2495727647,10267016450,42322763940,
%U A007743 174974139365
%N A007743 Number of achiral polyominoes with n cubical cells of the regular tiling with Schläfli symbol {4,3,4} (or polycubes).
%C A007743 A000162 but with both copies of each mirror-image deleted.
%C A007743 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 A007743 G. Thimm, <a href="/A007741/a007741.pdf">Emails to N. J. A. Sloane, Sep. 1994</a>
%F A007743 a(n) = A000162(n) - 2*A371397(n) = A038119(n) - A371397(n). - _Robert A. Russell_, Mar 21 2024
%Y A007743 A038119 = (A007743+A000162)/2, A007743 = 2*A038119 - A000162, A000162 = 2*A038119 - A007743.
%Y A007743 Cf. A000162 (oriented), A038119 (unoriented), A371397 (chiral), A001931 (fixed).
%Y A007743 Component symmetries: A376969, A376970, A376971, A376972, A376973, A376974, A376977, A376978, A376979, A376980, A376981, A376983, A376984, A376985, A376986, A376987, A376988, A376989, A376990, A376991, A377129, A377130.
%K A007743 nonn,nice
%O A007743 1,3
%A A007743 Arlin Anderson (starship1(AT)gmail.com)
%E A007743 a(13)-a(16) from Herman Jamke (hermanjamke(AT)fastmail.fm), May 05 2007
%E A007743 Changed "symmetric" to "mirror-symmetric" in the title by _George Sicherman_, Feb 21 2018
%E A007743 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 A007743 a(17)-a(22) from _John Mason_, Sep 19 2024