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A351299
a(n) is the number of distinct bipartitions of a solid triangular array of edge n, discounting inversions, reflections, and rotations.
0
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.
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
KEYWORD
nonn,more
AUTHOR
Tony Bartoletti, Feb 06 2022
STATUS
approved