A390993 Number of free polyaboloes (or polytans) with n cells, where the orientation of two triangles sharing a hypotenuse (making up a square) matters.

1, 3, 5, 21, 60, 253, 969, 4127, 17289, 74757, 323969, 1421323, 6266760, 27814218

Offset

1,2

Comments

For normal polyaboloes (A006074), two forms are considered equivalent if they differ only by the orientation of pairs of triangles sharing a hypotenuse.

Links

Table of n, a(n) for n=1..14.

Pontus von Brömssen, Illustration for n<=4.

Example

For n = 3 there are A006074(3) = 4 free polyaboloes. For one of them, namely the polyabolo consisting of two cells sharing a hypotenuse with a third cell attached along the short side, there are two versions counted here: the common hypotenuse of the first two cells can meet the third cell either at its right angle or at one of its acute angles. Hence, a(3) = 5.

Crossrefs

Cf. A006074, A390994 (one-sided), A390995 (fixed), A390996, A390999.

Sequence in context: A235136 A378071 A153862 * A266203 A264683 A286033

Adjacent sequences: A390990 A390991 A390992 * A390994 A390995 A390996

Keyword

nonn,more

Author

Pontus von Brömssen, Nov 27 2025

Extensions

a(14) from John Mason, Nov 29 2025

Status

approved