%I M1573 #49 Apr 15 2023 06:25:50
%S 0,0,0,1,2,6,9,23,38,90,147,341,564,1294,2148,4896,8195,18612,31349,
%T 70983,120357,271921,463712,1045559,1792582,4034832,6950579,15619507,
%U 27023509,60638559,105320716,236006955,411364068,920626423,1609836928
%N Number of axially symmetric polyominoes with n cells.
%C Number of polyominoes with n cells and exactly one line of reflection symmetry, where that one line is parallel to the grid. - _Joshua Zucker_, Mar 08 2008
%C The line of reflective symmetry may pass through the center of a square or a vertex of a square. These subsets are enumerated by A349328 and A349329 respectively. - _John Mason_, Feb 17 2022
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H John Mason, <a href="/A006746/b006746.txt">Table of n, a(n) for n = 1..50</a>
%H Tomás Oliveira e Silva, <a href="http://sweet.ua.pt/tos/animals.html">Enumeration of polyominoes</a>
%H 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 D. H. Redelmeier, <a href="/A056877/a056877.png">Table 3</a> of Counting polyominoes...
%F a(n) = A349328(n) + A349329(n/2) for even n, otherwise a(n) = A349328(n). - _John Mason_, Feb 17 2022
%Y Cf. A000105, A001168, A030227, A361625.
%Y Sequences classifying polyominoes by symmetry group: A000105, A006746, A006747, A006748, A006749, A056877, A056878, A142886, A144553, A144554, A349328, A349329.
%K nonn
%O 1,5
%A _N. J. A. Sloane_
%E Extended to n=28 by Tomás Oliveira e Silva