(Ignore this message)

"Let m(i,i) be the optimal solution when two officers cover i points and one of them is at the point i." Why do you want to include $m(i,i)$? "Each officer separately patrol a point" as said in your question, which is, as I understand, each officer patrols different points. Computing that one might not do extra harm, but it is certainly confusing and unnecessary, at least for me.

(Please Ignore my the message just above)

Can you paste an example where my recurrence formula does not work? It would be great if you can paste your code to some online IDE such as repl.it so that I can run your code and my code as well against some input.