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A390885

Number of free polyaboloes without any two triangles sharing a hypotenuse.

1, 2, 3, 6, 7, 13, 18, 31, 45, 76, 115, 190, 289, 472, 736, 1189, 1859, 2988, 4716, 7543, 11886, 18955, 30024, 47762, 75476, 119870, 189930, 301219, 476147, 754384, 1194531, 1890828, 2987615, 4726004, 7476387, 11818867, 18662392, 29487739, 46605846, 73603184

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Alternatively, free polyforms made of L-pipes connected end-to-end (not perpendicularly).

From Pontus von Brömssen, Nov 23 2025: (Start)

Other equivalent polyforms counted by a(n) (see linked illustration for n=6):

- free polyominoes consisting of n square cells, each of which has two adjacent chipped edges, preventing those edges from connecting to another cell;

- free polyarcs with n cells (A057787), all of which are quarter circles.

(End)

LINKS

Table of n, a(n) for n=1..40.

Pontus von Brömssen, Four illustrations of the 6-celled forms: L-pipes, polyominoes with chipped cells, polyaboloes with no two cells sharing a hypotenuse, polyarcs with quarter circle cells only.

Pontus von Brömssen, Illustration for n=8 (as polyarcs with quarter circle cells only).

Pontus von Brömssen, Illustration for n=10 (as polyarcs with quarter circle cells only).

Rhys Feltman, Polyels - Rhys’ Polyform Atlas.

Rhys Feltman, Polyels — Polypad.

Rhys Feltman, How each right isosceles triangle corresponds to an L.

Rhys Feltman, The subset of heptaboloes with no two triangles sharing a hypotenuse.

CROSSREFS