Question

[Extremely Long Question] Let 12|123|1234 be a set of 3 groups where different groups are seperated by |s. All the groups must contain consecutive numbers and the first group must start with 1. There are also rules for the following groups: 1. The first number follows the last number from the previous group (left), or 2. The group's numbers entirely consists of the previous group's last number. The number of numbers in each group doesn't change no matter how the numbers change inside the group (clumsy). How many combinations are there for
1. 1|11|111
2. 11|11|11|11 ?

Answer 1

The groups can also start with 1, creating another "run".