A355998 Number of fixed orthoplex n-ominoes with cell centers determining (n-2)-space.

1, 48, 1728, 62720, 2457600, 105815808, 5017600000, 261227298816, 14860167413760, 918839084134400, 61439672177393700, 4421589120000000000, 340976534987475000000, 28064307240230900000000, 2456376885785930000000000

Offset: 4

Author

Robert A. Russell, Jul 22 2022

Keywords

• 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. Two fixed polyominoes are identical only if one is a translation of the other.

Examples

			For A(4)=1, all 4 squares of the 2^2 space are used.
		

Crossrefs

Cf. A171860 (multidimensional), A036367 (unoriented), A036368 (chiral), A036369 (asymmetric).

Diagonal 2 of A355997.

Programs

Mathematica

Table[2^(n-3) n^(n-5) (n-2) (n-3)^2, {n,4,30}]

Formula

a(n) = 2^(n-3) * n^(n-5) * (n-2) * (n-3)^2.

a(n) ~ A171860(n) / 2.