A354380 Number of free pseudo-polytans (or polyfetts) with n cells.

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).

From Pontus von Brömssen, Nov 20 2025: (Start)

The following form is not included among the 90=a(3)-1 3-celled forms illustrated in the Sicherman link "Catalogue of Polyfetts":

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(End)

Links

Table of n, a(n) for n=1..9.

Sean A. Irvine, Java program (github)

George Sicherman, Catalogue of Polyfetts [Warning: one trifett is missing and counts are incorrect.]

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

Cf. A006074, A000105, A030222, A354403 (one-sided), A354405 (fixed).

Sequence in context: A347260 A267833 A389562 * A015467 A144783 A365217

Adjacent sequences: A354377 A354378 A354379 * A354381 A354382 A354383

Keyword

nonn,hard,more

Author

Aaron N. Siegel, May 24 2022

Status

approved