A355052 Number of oriented multidimensional n-ominoes with cell centers determining n-3 space.

1, 17, 131, 709, 3350, 14337, 57507, 218746, 803384, 2870707, 10044838, 34548917, 117224825, 393290329, 1307200931, 4310348599, 14116544717, 45959805027, 148860350902, 479938536114, 1541025955958, 4929773150983

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

Examples

			a(4)=1 because there is just one tetromino (with four cells aligned) in 1-space. a(5)=17 because there are 5 achiral and 6 chiral pairs of 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. A355053 (unoriented), A355054 (chiral), A355055 (achiral) A355056 (asymmetric), A191092 (fixed), A355047 (orthoplex), A195738 (Lunnon's DR).

Formula

a(n) = A355053(n) + A355054(n) = 2*A355053(n) - A355055(n) = 2*A355054(n) + A355055(n).

a(n) = A195738(n,n-3), the third diagonal of Lunnon's DR array.