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%I M1760 #31 Mar 22 2024 09:18:52
%S 1,1,2,7,23,112,607,3811,25413,178083,1279537,9371094,69513546,
%T 520878101,3934285874,29915913663
%N Number of n-celled solid polyominoes (or free polycubes, allowing mirror-image identification).
%C A000162 but with one copy of each mirror-image deleted.
%C From _R. J. Mathar_, Mar 19 2018: (Start)
%C We can split the numbers into an irregular table which lists in row n how many configurations have c contacts for c >= 0:
%C 1;
%C 0 1;
%C 0 0 2;
%C 0 0 0 6 1;
%C 0 0 0 0 21 2;
%C 0 0 0 0 0 91 19 2;
%C 0 0 0 0 0 0 484 110 12 1;
%C 0 0 0 0 0 0 0 2817 852 129 12 0 1;
%C 0 0 0 0 0 0 0 0 17788 6321 1166 132 5 1;
%C Row lengths are 1+A007818(n). Row sums are a(n).
%C (End)
%C Number of unoriented polyominoes with n cubical cells of the regular tiling with Schläfli symbol {4,3,4}. For unoriented polyominoes, chiral pairs are counted as one.- _Robert A. Russell_, Mar 21 2024
%D Computed by _Achim Flammenkamp_.
%D S. W. Golomb, Polyominoes. Scribner's, NY, 1965; second edition (Polyominoes: Puzzles, Packings, Problems and Patterns) Princeton Univ. Press, 1994.
%D W. F. Lunnon, Symmetry of cubical and general polyominoes, pp. 101-108 of R. C. Read, editor, Graph Theory and Computing. Academic Press, NY, 1972.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Achim Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/cgi-bin/cgiwrap/achim/index.cgi">Home page</a>
%H Kevin L. Gong, <a href="http://kevingong.com/Polyominoes/Enumeration.html">Polyominoes Home Page.</a>
%F a(n) = A000162(n) - A371397(n) = A371397(n) + A007743(n)). - _Robert A. Russell_, Mar 21 2024
%t A[s_Integer] := With[{s6 = StringPadLeft[ToString[s], 6, "0"]}, Cases[ Import["https://oeis.org/A" <> s6 <> "/b" <> s6 <> ".txt", "Table"], {_, _}][[All, 2]]];
%t A000162 = A@000162;
%t A007743 = A@007743;
%t a[n_] := (A007743[[n]] + A000162[[n]])/2;
%t a /@ Range[16] (* _Jean-François Alcover_, Jan 16 2020 *)
%Y A038119 = (A007743+A000162)/2, A007743 = 2*A038119 - A000162, A000162 = 2*A038119 - A007743.
%Y 32nd row of A366766.
%Y Cf. A000162 (oriented), A371397 (chiral), A007743 (achiral), A001931 (fixed).
%K nonn,hard,more,nice
%O 1,3
%A _N. J. A. Sloane_
%E More terms from Brendan Owen (brendan_owen(AT)yahoo.com), Jan 02 2002
%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 05 2007
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