A376971 Number of polycubes of size n and symmetry class G (full symmetry).

1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 2, 1, 1, 0, 0, 1, 2, 3, 1, 0, 0, 1, 3, 1, 1, 0, 0, 4, 5, 4, 1, 0, 0, 6, 7, 4, 3, 0, 0, 8, 10, 11, 3, 0, 0, 12, 14, 8, 5, 1, 0, 22, 21, 21, 7, 0, 0, 34, 32, 20, 12, 2, 0, 50, 48, 48, 16, 1, 1, 76, 69, 48, 27, 8, 1

Offset: 1

Author

John Mason, Oct 11 2024

Keywords

• nonn

Comments

See link "Counting free polycubes" for explanation of notation.

a(n) = 0 if and only if n is in the set {2, 3, 4, 5, 6, 9, 10, 11, 12, 14, 15, 16, 17, 21, 22, 23, 28, 29, 34, 35, 40, 41, 46, 47, 52, 53, 58, 59, 65, 70, 71, 77}. (See link "Polycubes with full symmetry".) - Pontus von Brömssen, Oct 12 2024

Conjecture: For n >= 62, a(n) > a(n-1) if and only if n is a multiple of 6. - Pontus von Brömssen, Oct 20 2024

Links

• Pontus von Brömssen, Table of n, a(n) for n = 1..233
• Pontus von Brömssen, Polycubes with full symmetry.
• John Mason, Counting free polycubes

Crossrefs

Cf. A000162, A038119, A142886 (polyominoes with full symmetry), A066288 (symmetric with rotations, group order 24).

Extensions

a(32)-a(36) from Pontus von Brömssen, Oct 14 2024

More terms from Pontus von Brömssen, Oct 20 2024