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A142886 Number of polyominoes with n cells that have the symmetry group D_8.

%I A142886 #47 Oct 14 2024 10:56:16
%S A142886 1,1,0,0,1,1,0,0,1,2,0,0,3,2,0,0,5,4,0,0,12,7,0,0,20,11,0,0,45,20,0,0,
%T A142886 80,36,0,0,173,65,0,0,310,117,0,0,664,216,0,0,1210,396,0,0,2570,736,0,
%U A142886 0,4728,1369,0,0,9976,2558,0,0,18468,4787,0,0,38840
%N A142886 Number of polyominoes with n cells that have the symmetry group D_8.
%C A142886 This is the largest possible symmetry group that a polyomino can have.
%C A142886 Polyominoes with such symmetry centered about square centers and vertices are enumerated by A351127 and A346800 respectively. - _John Mason_, Feb 16 2022
%H A142886 Robert A. Russell, <a href="/A142886/b142886.txt">Table of n, a(n) for n = 0..163</a>
%H A142886 Tomás Oliveira e Silva, <a href="http://sweet.ua.pt/tos/animals.html">Enumeration of polyominoes</a>
%H A142886 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 A142886 D. H. Redelmeier, <a href="/A056877/a056877.png">Table 3</a> of Counting polyominoes...
%H A142886 <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%F A142886 a(n) = A351127(n) + A346800(n/4) if n is a multiple of 4, otherwise a(n) = A351127(n). - _John Mason_, Feb 16 2022
%e A142886 The monomino has eight-fold symmetry. The tetromino with eight-fold symmetry is four cells in a square. The pentomino with eight-fold symmetry is a cell and its four adjacent cells.
%Y A142886 Sequences classifying polyominoes by symmetry group: A000105, A006746, A006747, A006748, A006749, A056877, A056878, A142886, A144553, A144554, A351127, A346800.
%Y A142886 Cf. A376971 (polycubes with full symmetry).
%K A142886 nonn
%O A142886 0,10
%A A142886 _N. J. A. Sloane_, Jan 01 2009
%E A142886 Name corrected by _Wesley Prosser_, Sep 06 2017
%E A142886 a(28) added by _Andrew Howroyd_, Dec 04 2018
%E A142886 More terms from _Robert A. Russell_, Jan 13 2019