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

1,19

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).

Sequence in context: A350847 A026821 A377334 * A039964 A369453 A340655

Adjacent sequences: A376968 A376969 A376970 * A376972 A376973 A376974

Keyword

nonn

Author

John Mason, Oct 11 2024

Extensions

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

More terms from Pontus von Brömssen, Oct 20 2024

Status

approved