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

6,1

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.

Links

Table of n, a(n) for n=6..27.

Formula

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

Example

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).

Sequence in context: A331862 A364634 A121121 * A228116 A091123 A037790

Adjacent sequences: A355044 A355045 A355046 * A355048 A355049 A355050

Keyword

easy,nonn

Author

Robert A. Russell, Jun 16 2022

Status

approved