I am trying to understand the following sequence:
A186783 -The diameter of the symmetric group generated by the transposition $(1,2)$ and both left and right rotations by $(1,2,\ldots,n)$. The sequence is $0,1,2,6,10,15,21,28,35,45,55,66,\ldots$ If we swap out the $2$ with a $3$ we would have the "triangular numbers", ${n+1 \choose 2}$. With that exception what would make us believe this sequence is not the "triangular numbers".