A351299 a(n) is the number of distinct bipartitions of a solid triangular array of edge n, discounting inversions, reflections, and rotations.

1, 2, 13, 128, 2864

Offset: 1

Author

Tony Bartoletti, Feb 06 2022

Keywords

• nonn
• more

Comments

Determined by exhaustive enumeration and testing. (Related to A061348 but discounting inversions.)

Discounting inversions allows only one of these two to be counted:

1 0

0 0 1 1

Related to A061348 (number of distinct binary labels of a solid triangular array of edge n, discounting reflections and rotations) except that inversions (swapping 0's and 1's) are also discounted.

Note that since the triangular numbers T(n) exhibit the odd/even pattern o o e e o o e e and only the odd triangular numbers are unable to support a 50/50 binary labeling, this sequence is A061348(n)/2 only for odd T(n), i.e., where floor((n-1)/2) is even.

Examples

			For n = 2, the a(2)=2 solutions are
    0     1
   0 0   0 0
		

Crossrefs

Cf. A061348.

Formula

a(n) = A061348(n)/2 where floor((n-1)/2) is even.