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 A006748 Number of diagonally symmetric polyominoes with n cells. (Formerly M0366) 25
 0, 0, 1, 0, 2, 2, 7, 5, 26, 22, 91, 79, 326, 301, 1186, 1117, 4352, 4212, 16119, 15849, 60174, 60089, 226146, 228426, 854803, 872404, 3247207, 3342579, 12389106, 12850662, 47448984, 49544820, 182338754, 191529007, 702807040, 742163178, 2716205709, 2882119756 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS This sequence counts polyominoes with exactly the symmetry group of order 2 generated by a single reflection about a diagonal. REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS John Mason, Table of n, a(n) for n = 1..50 (terms up to a(47) from Robert A. Russell) Tomás Oliveira e Silva, Enumeration of polyominoes D. H. Redelmeier, Counting polyominoes: yet another attack, Discrete Math., 36 (1981), 191-203. D. H. Redelmeier, Table 3 of Counting polyominoes... Toshihiro Shirakawa, Harmonic Magic Square, pp 3-4: Enumeration of Polyominoes considering the symmetry, April 2012. FORMULA a(n) = (A346800(n) - A142886(n)) / 2 - A056878(n). - Robert A. Russell, Aug 25 2021 CROSSREFS Cf. A000105, A001168, A006746, A056877, A006748, A056878, A006747. Sequences classifying polyominoes by symmetry group: A000105, A006746, A006747, A006748, A006749, A056877, A056878, A142886, A144553, A144554. Sequence in context: A223000 A058625 A300126 * A193548 A131049 A126851 Adjacent sequences: A006745 A006746 A006747 * A006749 A006750 A006751 KEYWORD nonn AUTHOR N. J. A. Sloane EXTENSIONS Extended to n=28 by Tomás Oliveira e Silva STATUS approved

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Last modified September 21 11:30 EDT 2023. Contains 365501 sequences. (Running on oeis4.)