cp's OEIS Frontend

A006748 Number of diagonally symmetric polyominoes with n cells.

%I A006748 M0366 #54 Apr 16 2023 12:32:40
%S A006748 0,0,1,0,2,2,7,5,26,22,91,79,326,301,1186,1117,4352,4212,16119,15849,
%T A006748 60174,60089,226146,228426,854803,872404,3247207,3342579,12389106,
%U A006748 12850662,47448984,49544820,182338754,191529007,702807040,742163178,2716205709,2882119756
%N A006748 Number of diagonally symmetric polyominoes with n cells.
%C A006748 This sequence counts polyominoes with exactly the symmetry group of order 2 generated by a single reflection about a diagonal.
%D A006748 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006748 John Mason, <a href="/A006748/b006748.txt">Table of n, a(n) for n = 1..50</a> (terms up to a(47) from Robert A. Russell)
%H A006748 Tomás Oliveira e Silva, <a href="http://sweet.ua.pt/tos/animals.html">Enumeration of polyominoes</a>
%H A006748 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 A006748 D. H. Redelmeier, <a href="/A056877/a056877.png">Table 3</a> of Counting polyominoes...
%H A006748 Toshihiro Shirakawa, <a href="https://www.gathering4gardner.org/g4g10gift/math/Shirakawa_Toshihiro-Harmonic_Magic_Square.pdf">Harmonic Magic Square, pp 3-4: Enumeration of Polyominoes considering the symmetry</a>, April 2012.
%F A006748 a(n) = (A346800(n) - A142886(n)) / 2 - A056878(n). - _Robert A. Russell_, Aug 25 2021
%Y A006748 Cf. A000105, A001168, A006746, A056877, A006748, A056878, A006747.
%Y A006748 Sequences classifying polyominoes by symmetry group: A000105, A006746, A006747, A006748, A006749, A056877, A056878, A142886, A144553, A144554.
%K A006748 nonn
%O A006748 1,5
%A A006748 _N. J. A. Sloane_
%E A006748 Extended to n=28 by _Tomás Oliveira e Silva_