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%I #7 May 25 2022 11:48:07
%S 1,10,91,1432,23547,416177,7544247,139666895,2623895224
%N Number of free pseudo-polytans with n cells.
%C A pseudo-polytan is a planar figure consisting of n isosceles right triangles joined either edge-to-edge or corner-to-corner, in such a way that the short edges of the triangles coincide with edges of the square lattice. Two figures are considered equivalent if they differ only by a rotation or reflection.
%C The pseudo-polytans are constructed in the same way as ordinary polytans (A006074), but allowing for corner-connections. Thus they generalize polytans in the same way that pseudo-polyominoes (aka polyplets, A030222) generalize ordinary polyominoes (A000105).
%H Aaron N. Siegel, <a href="/A354380/a354380.png">Illustration showing a(2) = 10</a>. The color of each figure corresponds to its number of symmetries.
%e a(2) = 10, because there are 10 ways of adjoining two isosceles right triangles: 3 distinct edge-to-edge joins (cf. A006074), and 7 distinct corner-to-corner joins.
%Y Cf. A006074, A000105, A030222.
%K nonn,hard,more
%O 1,2
%A _Aaron N. Siegel_, May 24 2022
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