In this task, you are given inputs i,j, and A, where i and j are integers and A is a list. You need to return the sum of all the numerical elements in the list A between the positions i and j (including positions i and j). Return 0 if no numerical element is present in the list between the given ranges. i and j will be non-negative, and will always have a value less than the length of A. i will always be less than j.

Example Input: 19, 19, ['4147', '1103', '5749', 'c', '5103', '3491', '4511', '197', 'T', '1601', 'J', 'c', '1309', 'a', '607', 'p', 'C', '9473', '5221', 'D', 'U', 'O', '5013']
Example Output: 5221

Example Input: 5, 9, ['125', 'A', 'E', 'X', 'j', '319', 'm', '7037', 'g', 'D', 'g', '6737', 'z', '5249']
Example Output: 7356

Example Input: 22, 30, ['C', 'n', 'i', '6399', '9373', 'P', '2371', 'C', '5669', 'O', '1191', 'Y', '4857', '7459', 'v', 'S', '611', 'e', 'j', '5859', 'w', '6115', 'b', '3431', 'C', '9089', 'C', '3063', '9419', '6511']
Example Output:
37628