%I #19 Aug 01 2022 20:00:05

%S 1,2,13,128,2864

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

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

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

%C 1 0

%C 0 0 1 1

%C 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.

%C 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.

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

%e For n = 2, the a(2)=2 solutions are

%e 0 1

%e 0 0 0 0

%Y Cf. A061348.

%K nonn,more

%O 1,2

%A _Tony Bartoletti_, Feb 06 2022