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A006749 Number of asymmetric polyominoes with n cells.

%I A006749 M3906 #38 Mar 21 2024 21:02:38
%S A006749 0,0,0,1,5,20,84,316,1196,4461,16750,62878,237394,899265,3422111,
%T A006749 13069026,50091095,192583152,742560511,2870523142,11122817672,
%U A006749 43191285751,168046076423,654997492842,2557223459805,9999080270766,39152997087077,153511067364760
%N A006749 Number of asymmetric polyominoes with n cells.
%C A006749 This sequence counts polyominoes whose symmetry group has order 1.
%D A006749 A. R. Conway and A. J. Guttmann, On two-dimensional percolation, J. Phys. A: Math. Gen. 28(1995) 891-904.
%D A006749 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006749 John Mason, <a href="/A006749/b006749.txt">Table of n, a(n) for n = 1..50</a> (This version corrects erroneous values from a(44) onwards in previous version.)
%H A006749 Tomás Oliveira e Silva, <a href="http://sweet.ua.pt/tos/animals.html">Enumeration of polyominoes</a>
%H A006749 T. R. Parkin, L. J. Lander, and D. R. Parkin, <a href="/A000104/a000104.pdf">Polyomino Enumeration Results</a>, presented at SIAM Fall Meeting, 1967, and accompanying letter from T. J. Lander (annotated scanned copy). See page 21.
%H A006749 D. H. Redelmeier, <a href="http://dx.doi.org/10.1016/0012-365X(81)90237-5">Counting polyominoes: yet another attack</a>, Discrete Math., 36 (1981), 191-203.
%H A006749 D. H. Redelmeier, <a href="/A056877/a056877.png">Table 3</a> of Counting polyominoes...
%F A006749 a(n) + A259090(n) = A000105(n). - _R. J. Mathar_, Sep 29 2021
%Y A006749 Cf. A000105, A001168, A006746, A056877, A006748, A056878, A006747, A006749.
%Y A006749 Sequences classifying polyominoes by symmetry group: A000105, A006746, A006747, A006748, A006749, A056877, A056878, A142886, A144553, A144554.
%K A006749 nonn,nice
%O A006749 1,5
%A A006749 _N. J. A. Sloane_
%E A006749 Extended to n=28 by Tomás Oliveira e Silva.