$$
\newcommand{\arccot}{\operatorname{arccot}}
\arccot(2)+\arccot(8)+\arccot(18)+\arccot(32)+\ldots=?
$$
this the question.
First find a relation of $2,8,18,32,\ldots$
$$
a_1=2, a_2=8, a_3=18, a_4=32 ,\ldots
$$
it seems the difference between them $6,10,14,\ldots\ (+4)$ so maybe $a_5=50,a_6=72 ,\ldots$
but what next?
according to OEIS, this sequence is the mean of two triangular numbers such as $$ \frac{1+3}{2},\frac{6+10}{2},\frac{15,21}{2},\ldots $$ and what is the next step?
then I tried to rewrite $$ \arccot(2)+\arccot(8)+\arccot(18)+\arccot(32)+\ldots=\\ \arctan(\frac1{2})+\arctan(\frac1{8})+\arctan(\frac1{18})+ \arctan(\frac1{32})+\ldots $$ than find the partial sum with desmos https://www.desmos.com/calculator/k7xv7l8d8z
it seems bounded, but got no clue to solve it analytically.
Any help will be appreciated.