10.4, 11.3 Given N≥3 points enumerated with 1, 2, ..., N. Each two numbers are connected by mean of arrow from a lesser number to a greater one. A coloring of all arrows into red and blue is called monochromatic iff for any numbers A and B there are no two monochromatic paths from A to B of different colors. Find the number of monochromatic colorings.
(I. Bogdanov, G. Chelnokov) inductioncombinatorics proposedcombinatorics