This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A351299 #19 Aug 01 2022 20:00:05 %S A351299 1,2,13,128,2864 %N A351299 a(n) is the number of distinct bipartitions of a solid triangular array of edge n, discounting inversions, reflections, and rotations. %C A351299 Determined by exhaustive enumeration and testing. (Related to A061348 but discounting inversions.) %C A351299 Discounting inversions allows only one of these two to be counted: %C A351299 1 0 %C A351299 0 0 1 1 %C A351299 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 A351299 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 A351299 a(n) = A061348(n)/2 where floor((n-1)/2) is even. %e A351299 For n = 2, the a(2)=2 solutions are %e A351299 0 1 %e A351299 0 0 0 0 %Y A351299 Cf. A061348. %K A351299 nonn,more %O A351299 1,2 %A A351299 _Tony Bartoletti_, Feb 06 2022