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A056878 Number of polyominoes with n cells, symmetric about diagonal 2.

%I A056878 #32 Feb 17 2022 20:34:42
%S A056878 0,0,0,0,0,0,1,1,0,1,2,3,3,5,6,14,9,20,20,56,32,80,64,224,114,315,217,
%T A056878 863,397,1234,751,3331,1400,4816,2632,12815,4973,18792,9349,49400,
%U A056878 17810,73338,33557,190643,64309,286368,121511,737532,233891,1119215,443271,2859154
%N A056878 Number of polyominoes with n cells, symmetric about diagonal 2.
%C A056878 The sequence refers to those polyominoes having reflective symmetry on both diagonals, consequent 180-degree rotational symmetry, but without 90-degree rotational symmetry. Such polyominoes with rotational symmetry symmetry centered about square centers and vertices are enumerated by A351159 and A351160 respectively. - _John Mason_, Feb 17 2022
%H A056878 Robert A. Russell, <a href="/A056878/b056878.txt">Table of n, a(n) for n = 1..87</a>
%H A056878 Tomás Oliveira e Silva, <a href="http://sweet.ua.pt/tos/animals.html">Enumeration of polyominoes</a>
%H A056878 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 A056878 D. H. Redelmeier, <a href="/A056877/a056877.png">Table 3</a> of Counting polyominoes...
%F A056878 a(n) = A351159(n) + A351160(n/2) for even n, otherwise a(n) = A351159(n). - _John Mason_, Feb 17 2022
%e A056878 For a(7)=1, the heptomino with exactly fourfold symmetry and axes of symmetry parallel to the diagonals of the cells is composed of two 2 X 2 squares with one cell in common. For a(8)=1, the octomino is composed of a 2 X 2 square and the four cells adjacent to two nonadjacent cells of that square.
%Y A056878 Cf. A000105, A001168, A006746, A056877, A006748, A056878, A006747, A006749.
%Y A056878 Sequences classifying polyominoes by symmetry group: A000105, A006746, A006747, A006748, A006749, A056877, A056878, A142886, A144553, A144554, A351159, A351160.
%K A056878 nonn
%O A056878 1,11
%A A056878 _N. J. A. Sloane_, Sep 03 2000
%E A056878 More terms from _Robert A. Russell_, Jan 18 2019