A383799 Irregular triangle: T(n,k) gives the number of k-polysticks on edges of the n-cube up to rotational symmetries of the n-cube, with 0 <= k <= A001787(n).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 6, 14, 24, 32, 25, 13, 5, 1, 1, 1, 1, 1, 4, 10, 35, 131, 510, 1932, 7123, 24466, 76829, 214685, 518820, 1050433, 1727591, 2273998, 2446653, 2212119, 1709579, 1143416, 663450, 335186, 146371, 55327, 17767, 4898, 1103, 226, 35, 7, 1, 1

Offset: 1

Author

Peter Kagey, May 10 2025

Keywords

• nonn
• tabf

Comments

Row 3 gives the number of polyforms with n cells on the faces of a rhombic dodecahedron up to rotation.

Examples

			Table begins:
n\k| 0  1  2  3   4   5    6    7     8     9     10     11      12
---+----------------------------------------------------------------
  1| 1, 1;
  2| 1, 1, 1, 1,  1;
  3| 1, 1, 1, 4,  6, 14,  24,  32,   25,   13,     5,     1,      1;
  4| 1, 1, 1, 4, 10, 35, 131, 510, 1932, 7123, 24466, 76829, 214685, ...
		

Links

• Wikipedia, Hypercube
• Wikipedia, Polystick

Crossrefs

Cf. A001787, A222186.

Cf. A333333 (analogous with reflectional symmetries allowed).

Formula

A222186(n) = Sum_{k=0..n*2^(n-1)} T(n,k) - Sum_{k=0..(n-1)*2^(n-2)} T(n-1,k) for n >= 2. - Pontus von Brömssen, May 12 2025

Extensions

a(30)-a(40) from Pontus von Brömssen, May 14 2025

a(41)-a(53) from Pontus von Brömssen, Jun 11 2025