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A354380
Number of free pseudo-polytans with n cells.
4
1, 10, 91, 1432, 23547, 416177, 7544247, 139666895, 2623895224
OFFSET
1,2
COMMENTS
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.
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).
LINKS
Aaron N. Siegel, Illustration showing a(2) = 10. The color of each figure corresponds to its number of symmetries.
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Aaron N. Siegel, May 24 2022
STATUS
approved