A354380 Number of free pseudo-polytans with n cells.

1, 10, 91, 1432, 23547, 416177, 7544247, 139666895, 2623895224

Offset: 1

Author

Aaron N. Siegel, May 24 2022

Keywords

• nonn
• hard
• more

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).

Examples

			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.
		

Links

• Aaron N. Siegel, Illustration showing a(2) = 10. The color of each figure corresponds to its number of symmetries.

Crossrefs

Cf. A006074, A000105, A030222.