I have been looking at some simpler versions where digits sum < 9 example: from 1 to $10^4$ how many sum to 5? using repeated combinations $\binom{5+5−1}{5}=\binom{9}{5}=126$ however the given answer is 56
does a generalized version (formula) exist where R = sum of digits ; N = number of digits. $ A \leq N \leq B $
in the example above$ R = 5; N = 5; A = 1; B = 5; $