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

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

Cf. A000012 (I-pipes), A000105 (X-pipes), A000577 (Y-pipes with three 120-degree angles), A390515 (T-pipes).

Cf. A006074 (polyaboloes), A057787 (polyarcs).

Sequence in context: A330145 A183558 A328164 * A294916 A233423 A328024

Adjacent sequences: A390882 A390883 A390884 * A390886 A390887 A390888

Keyword

nonn

Author

Rhys Feltman, Nov 22 2025

Extensions

a(8)-a(32) from Pontus von Brömssen, Nov 23 2025

a(33)-a(40) from Christian Sievers, Nov 25 2025

Status

approved