Matematické Fórum

Skrytý text:

1) C1 must be first or last
2) if Ci and Cj are succesive placed children and Ci>Cj then the children Ck placed after Cj must be less then Cj - so thare must be decreasing sequence Ci>Cj>Ck
3) From this we can deduce that we are counting sequences with local minima only possible on the boundaries - so the sequence is monotone or can be separated into two monotone sequences - one increasing and the second decreasing
4) From 3 we can deduce that separation point is C6, so we can consider separate cases - when C6 is first, second, third - and it separates two monotone sequences - and monotone sequences can be treated symmetrically (increasing and decreasing) and monotone sequence is in bijection with the subset - so the count will be something like sum of - and this can be, I guess, expressed in closed form (no sum).