A333418 Irregular triangle: T(n,k) gives the number of ways to 2-color k edges of the n-cube up to rotation and reflection, with 0 <= k <= A001787(n).

1, 1, 1, 1, 2, 1, 1, 1, 1, 4, 9, 18, 24, 30, 24, 18, 9, 4, 1, 1, 1, 1, 6, 24, 140, 604, 2596, 9143

Offset: 1

Author

Peter Kagey, Mar 20 2020

Keywords

• nonn
• tabf
• more

Comments

Conjecture: All rows are unimodal (increasing, then decreasing).

Each row is a palindrome.

A333333 is analogous with the restriction that the colorings must be connected.

Examples

			Table begins:
n\k| 0  1   2   3    4    5     6     7   8  9 10 11 12 ...
---+-------------------------------------------------------
  1| 1, 1;
  2| 1, 1,  2,  1,   1;
  3| 1, 1,  4,  9,  18,  24,   30,   24, 18, 9, 4, 1, 1;
  4| 1, 1,  6, 24, 140, 604, 2596, 9143, ...
  5| 1, 1,  8, 50, 608, ...
  6| 1, 1, 10, 89, ...
		

Links

• Mathematics Stack Exchange, Number of 2-colorings of edges of the n-dimensional cube?.
• Wikipedia, Hypercube

Crossrefs

Row sums are A333444.

Cf. A001787, A060530, A199406, A331359, A333444, A333333.

Formula

T(n,k) >= ceiling(binomial(A001787(n),k)/A000165(n)).