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

1,2

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.

Links

Table of n, a(n) for n=1..5.

Formula

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

Example

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

Crossrefs

Cf. A061348.

Sequence in context: A290219 A057065 A259611 * A215624 A247365 A107721

Adjacent sequences: A351296 A351297 A351298 * A351300 A351301 A351302

Keyword

nonn,more

Author

Tony Bartoletti, Feb 06 2022

Status

approved