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

1,5

Comments

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

Links

Table of n, a(n) for n=1..22.

Formula

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

Example

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).

Sequence in context: A300583 A060774 A043026 * A125837 A065088 A202364

Adjacent sequences: A371394 A371395 A371396 * A371398 A371399 A371400

Keyword

nonn,more

Author

Robert A. Russell, Mar 21 2024

Extensions

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

Status

approved