A355050 Number of achiral orthoplex n-ominoes with cell centers determining n-3 space.

3, 10, 46, 215, 1221, 6384, 31153, 140320, 596779, 2416833, 9417531, 35541184, 130684964, 470159267, 1660756778, 5775367751, 19816896743, 67213026352, 225673938496, 751028439756, 2479882044054, 8131813096411

Offset: 6

Author

Robert A. Russell, Jun 16 2022

Keywords

• nonn
• easy

Comments

Orthoplex polyominoes are connected sets of cells of regular tilings with Schläfli symbols {}, {4}, {3,4}, {3,3,4}, {3,3,3,4}, etc. These are tilings of regular orthoplexes projected on their circumspheres. Orthoplex polyominoes are equivalent to multidimensional polyominoes that do not extend more than two units along any axis, i.e., fit within a 2^d cube. This sequence is obtained using the first formula below. An achiral polyomino is identical to its reflection.

Examples

			a(6)=3 because there are 3 hexominoes in 2^3 space, all achiral. The two vacant cells share just a face, an edge, or a vertex.
		

Crossrefs

Cf. A355047 (oriented), A355048 (unoriented), A355049 (chiral), A355051 (asymmetric), A355055 (multidimensional).

Formula

a(n) = A355048(n) - A355049(n) = 2*A355048(n) - A355047(n) = A355047(n) - 2*A355049(n).