MathDB

Freddy the Frog is situated at 1 on an infinitely long number line. On day

n

, where

n\ge 1

, Freddy can choose to hop 1 step to the right, stay where he is, or hop

k

steps to the left, where

k

is an integer at most

n+1

. After day 5, how many sequences of moves are there such that Freddy has landed on at least one negative number?
Proposed by Andy Xu

24