A355055 Number of achiral multidimensional n-ominoes with cell centers determining n-3 space.

1, 5, 23, 115, 668, 3401, 16469, 74410, 317612, 1287147, 5015932, 18920467, 69496943, 249618639, 879998839, 3053446651, 10452089459, 35360685297, 118416973230, 393038044024, 1294335897888, 4232938101229, 13757913332396

Offset: 4

Author

Robert A. Russell, Jun 16 2022

Keywords

• nonn
• easy

Comments

Multidimensional polyominoes are connected sets of cells of regular tilings with Schläfli symbols {oo}, {4,4}, {4,3,4}, {4,3,3,4}, etc. Each tile is a regular orthotope (hypercube). This sequence is obtained using the first formula below. An achiral polyomino is identical to its reflection.

Examples

			a(4)=1 as there is only one tetromino in one-space. a(5)=5 because there are 5 achiral pentominoes in 2-space, excluding the 1-D straight pentomino.
		

Links

• W. F. Lunnon, Counting multidimensional polyominoes. Computer Journal 18 (1975), no. 4, pp. 366-367.

Crossrefs

Cf. A355052 (oriented), A355053 (unoriented), A355054 (chiral), A355056 (asymmetric), A191092 (fixed), A355050 (orthoplex), A195738 (Lunnon's DR), A049430 (Lunnon's DE).

Formula

a(n) = A355053(n) - A355054(n) = 2*A355053(n) - A355052(n) = A355052(n) - 2*A355054(n).

a(n) = 2*A049430(n,n-3) - A195738(n,n-3), Lunnon's DE and DR arrays.