A365559 Number of free n-polysticks (or polyedges) in 3 dimensions.

1, 2, 7, 28, 160, 1085, 8403, 69824, 607988, 5448444, 49846437, 462977928

Offset: 1

Author

Pontus von Brömssen, Sep 09 2023

Keywords

• nonn
• hard
• more

Comments

a(1)-a(8) verified and a(9)-a(10) computed by John Mason.

Examples

			There are a(3) = 7 free 3-polysticks in 3 dimensions: A019988(3) = 5 properly 1- or 2-dimensional (straight, "U", "T", "L", and skew, similar to the 5 tetrominoes) and 2 properly 3-dimensional (one path-like and one with a vertex of degree 3).
		

Links

• Ishino Keiichiro, Polyedge, Puzzle will be played, 2009.
• Index entries for sequences related to polyominoes.

Crossrefs

Sum of first three columns of A365566.

Cf. A019988 (2 dimensions), A365560 (fixed), A365561 (4 dimensions), A365563 (5 dimensions), A365565 (arbitrary dimension).

14th row of A366766.

Extensions

a(11) derived from Ishino Keiichiro's website (sum of 2-sided 2D-edges and 3D-edges), added by Pontus von Brömssen, Dec 21 2023

a(12) from John Mason, Mar 07 2025