A355047 Number of oriented orthoplex n-ominoes with cell centers determining n-3 space.

3, 26, 198, 1095, 5259, 22678, 91887, 354442, 1320089, 4780355, 16943165, 59007970, 202599228, 687342673, 2308586154, 7687335917, 25407923029, 83430814454, 272382655862, 884706011664, 2860304423466, 9208948000393

Offset: 6

Author

Robert A. Russell, Jun 16 2022

Keywords

• easy
• nonn

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. For oriented polyominoes, chiral pairs are counted as two.

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. A355048 (unoriented), A355049 (chiral), A355050 (achiral) A355051 (asymmetric), A355052 (multidimensional).

Formula

a(n) = A355048(n) + A355049(n) = 2*A355048(n) - A355050(n) = 2*A355049(n) + A355050(n).