A371397 Number of chiral pairs of polyominoes with n cubical cells of the regular tiling with Schläfli symbol {4,3,4}.

0, 0, 0, 1, 6, 54, 416, 3111, 22898, 168460, 1242985, 9227333, 68949103, 518618196, 3925228596, 29879207817, 228630283775, 1757699977107, 13570824097968, 105182547181534, 818093724437992, 6383353614308209

Offset: 1

Author

Robert A. Russell, Mar 21 2024

Keywords

• nonn
• more

Comments

Also called polycubes. Each member of a chiral pair is a reflection but not a rotation of the other.

Examples

			Polyominoes with cell centers at (0,0,0), (0,0,1), (0,1,1), (1,1,1) and (0,0,0), (0,1,0), (0,1,1), (1,1,1) are a chiral pair.
		

Crossrefs

Cf. A000162 (oriented), A038119 (unoriented), A007743 (achiral), A001931 (fixed).

Component symmetries: A376964, A376965, A376966, A376967, A376968, A376975, A376976, A376982, A377127, A377128, A377131.

Formula

a(n) = A000162(n) - A038119(n) = (A000162(n) - A007743(n))/2 = A038119(n) - A007743(n).

Extensions

a(17)-a(22) from John Mason, Sep 19 2024