Calculate the number of combinations of a sequence of numbers in a particular order I have a problem solving coding challenge when I have to calculate the number of combinations, numbers from 0 to 9, with the length n, with 2 rules -

- The first number cannot be 0

- Every other number can be 0 or must be divisible by the previous number (number 1 can not be used as divisor), for example [5.0], [1,0] or [2,8], [4,8], [3,6]

For example, if the length n were 2, number of combinations would be 23 - [1,0]...[9,0] + [2,4], [2,6], [2,8], [3,6], [3,9], [4,8] + [2,2]...[9,9]



The resulting response can be code in some programming language or a formula to calculate answer
Can you solve the problem for $n=1$?
Can you deduce the answer for $k+1$, if you know the answer for $k$? 
(hint: you need an $n\times 10$ table, the $k$-th row devoted for problem size $k$, the columns for partial answers...)

ps: I think that the answer is $9+0+1+1+2+1+3+1+3+2=23$ for n=2 (and 125 for $n=3$)

0: 10,...,90
1: - 
2: 22
3: 33
4: 24,44
5: 55
6: 26,36,66
7: 77
8: 28,48,88
9: 39,99