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

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

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..11.

Ishino Keiichiro, Polyedge, Puzzle will be played, 2009.

Index entries for sequences related to polyominoes.

Example

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).

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.

Sequence in context: A362084 A296726 A334613 * A123026 A013011 A013181

Adjacent sequences: A365556 A365557 A365558 * A365560 A365561 A365562

Keyword

nonn,hard,more

Author

Pontus von Brömssen, Sep 09 2023

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

Status

approved